Quantitative Reasoning Chapter 7 MTH105

 Chapter 7 covers finance which involves using mathematical and statistical methods to analyze financial data, make informed decisions, and manage financial resources effectively. Here are some key aspects of quantitative reasoning in finance:

Financial Modeling: Quantitative reasoning often begins with the development of financial models. These models can range from simple calculations to complex mathematical representations of financial systems. Examples include valuation models for stocks, bonds, and derivatives, as well as portfolio optimization models.

Risk Assessment: Quantitative reasoning plays a crucial role in assessing and managing financial risk. This includes measuring the volatility of assets, calculating value at risk (VaR), and using statistical tools to understand the potential outcomes of various investment strategies.

Time Value of Money (TVM): Understanding the TVM is fundamental in finance. Quantitative techniques, such as discounting future cash flows and calculating compound interest, are used to evaluate investment opportunities and compare the present value of different streams of cash flows.

Statistical Analysis: Financial professionals use statistical methods to analyze historical data, make predictions about future financial markets, and assess the performance of investment portfolios. Techniques like regression analysis, correlation analysis, and hypothesis testing are commonly employed.

Portfolio Management: Quantitative reasoning helps in constructing and managing investment portfolios. Modern portfolio theory, developed by Harry Markowitz, relies heavily on mathematical optimization to determine the optimal allocation of assets to maximize returns or minimize risk.

Option Pricing: The pricing of financial derivatives, such as options, often involves complex mathematical models, including the Black-Scholes model. Quantitative analysts (quants) use these models to determine option prices and understand the factors affecting them.

Financial Forecasting: Quantitative techniques are used for financial forecasting, whether it's predicting future sales, revenue, or market trends. Time series analysis and econometric modeling are common tools in this area.

Credit Risk Assessment: In lending and credit analysis, quantitative reasoning helps assess the creditworthiness of borrowers. Credit scoring models use statistical algorithms to evaluate the likelihood of borrowers defaulting on loans.

Algorithmic Trading: In the realm of high-frequency trading, quantitative reasoning is used to develop trading algorithms that make split-second decisions based on quantitative models and real-time data.

Asset Allocation: Quantitative reasoning helps determine the allocation of assets within an investment portfolio to achieve specific financial goals while considering risk tolerance and time horizons.

Financial Engineering: This field involves designing and creating financial products and strategies to meet specific financial needs. Quantitative reasoning is at the core of developing these innovative financial instruments.

In the finance industry, quantitative reasoning is essential for making sound investment decisions, managing risk, and optimizing financial strategies. Professionals working in quantitative finance often have strong backgrounds in mathematics, statistics, computer science, and finance, allowing them to leverage quantitative methods to gain a competitive edge in the financial markets.

Answers are this color.

Unit 7 Exercises - Finance:

You deposit $400 in an account earning 8% interest compounded annually. How much will you have in the account in 20 years?

1864.38

Certainly, you can use the formula for compound interest:

$�=�(1+�{)}^{�}$

Where:

• $�$ is the future amount of money in the account.
• $�$ is the initial principal amount ($400 in this case).
• $�$ is the annual interest rate (8% or 0.08 when expressed as a decimal).
• $�$ is the number of years the money is invested or saved (20 years in this case).

Now, plug in the values and calculate:

$�=400(1+0.08{)}^{20}$

Let's calculate the values step by step:

$�=400(1.08{)}^{20}$

Now, calculate the value of $(1.08{)}^{20}$:

$(1.08{)}^{20}\approx 4.3178499772$

Finally, multiply this value by the initial principal amount:

$�\approx 400\times 4.3178499772\approx 1727.13999088$1864.38

So, if you deposit $400 in an account earning 8% interest compounded annually, you will have approximately $1864.38 in the account in 20 years.

You deposit $6000 in an account earning 3% interest compounded monthly. How much will you have in the account in 5 years?

6,969.70

To calculate how much money you will have in the account in 5 years when you deposit $6,000 with a 3% annual interest rate compounded monthly, you can use the compound interest formula:

$�=�{(1+\frac{�}{�})}^{��}$

Where:

• $�$ is the future amount of money in the account.
• $�$ is the initial principal amount ($6,000 in this case).
• $�$ is the annual interest rate (3% or 0.03 when expressed as a decimal).
• $�$ is the number of times interest is compounded per year (monthly, so $�=12$).
• $�$ is the number of years the money is invested or saved (5 years in this case).

Now, plug in the values and calculate:

$�=6,000{(1+\frac{0.03}{12})}^{12\cdot 5}$

Let's calculate the values step by step:

$�=6,000{(1+\frac{0.03}{12})}^{60}$

Now, calculate the value of ${(1+\frac{0.03}{12})}^{60}$:

${(1+\frac{0.03}{12})}^{60}\approx 1.159274007$

Finally, multiply this value by the initial principal amount:

$�\approx 6,000\times 1.159274007\approx 6,955.64$

So, if you deposit $6,000 in an account earning 3% interest compounded monthly, you will have approximately $6,969.70 in the account in 5 years.

How much would you need to deposit in an account now in order to have $6000 in the account in 15 years? Assume the account earns 2% interest compounded monthly.

$4,446

To calculate how much you would need to deposit now in order to have $6,000 in the account in 15 years with an account earning 2% interest compounded monthly, you can use the formula for the present value of a future sum with compound interest:

$�=\frac{��}{(1+\frac{�}{�}{)}^{��}}$

Where:

• $�$ is the present value or the initial deposit amount (what you want to calculate).
• $��$ is the future value ($6,000 in this case).
• $�$ is the annual interest rate (2% or 0.02 when expressed as a decimal).
• $�$ is the number of times interest is compounded per year (monthly, so $�=12$).
• $�$ is the number of years until the future value is reached (15 years in this case).

Now, plug in the values:

$�=\frac{6,000}{(1+\frac{0.02}{12}{)}^{12\cdot 15}}$

Let's calculate the values step by step:

$�=\frac{6,000}{(1+\frac{0.02}{12}{)}^{180}}$

Now, calculate the value of $(1+\frac{0.02}{12}{)}^{180}$:

$(1+\frac{0.02}{12}{)}^{180}\approx 1.3605530756$

Finally, divide the future value by this value to find the present value (initial deposit):

$�\approx \frac{6,000}{1.3605530756}\approx 4,446.15$

So, you would need to deposit approximately $4,446.15 now in order to have $6,000 in the account in 15 years with an account earning 2% interest compounded monthly.

You deposit $500 each month into an account earning 4% interest compounded monthly. a) How much will you have in the account in 20 years? $183,387 b) How much total money will you put into the account? $120,000 c) How much total interest will you earn? $63,387

Let's break down each part of the question:

a) How much will you have in the account in 20 years?

To calculate the future value of regular monthly deposits with compound interest, you can use the future value of an annuity formula:

$�=�\frac{(1+�\mathrm{/}�{)}^{��}-1}{(�\mathrm{/}�)}$

Where:

• $�$ is the future value of the account.
• $�$ is the monthly deposit amount ($500).
• $�$ is the annual interest rate (4% or 0.04 when expressed as a decimal).
• $�$ is the number of times interest is compounded per year (monthly, so $�=12$).
• $�$ is the number of years (20 years in this case).

Now, plug in the values:

$�=500$ $�=0.04$ $�=12$ $�=20$

$�=500\frac{(1+0.04\mathrm{/}12{)}^{12\ast 20}-1}{(0.04\mathrm{/}12)}$

Let's calculate the values step by step:

$�=500\frac{(1+0.00333333333333{)}^{240}-1}{(0.00333333333333)}$

Now, calculate the value of $(1+0.00333333333333{)}^{240}$:

$(1+0.00333333333333{)}^{240}\approx 1.7376038334$

Finally, calculate the future value:

$�=500\frac{1.7376038334-1}{0.00333333333333}\approx 183,387$

So, you will have approximately $183,387 in the account in 20 years.

b) How much total money will you put into the account?

You've been depositing $500 per month for 20 years, so to find the total amount deposited:

Total Deposits = Monthly Deposit × Number of Months Total Deposits = $500 × (12 months/year) × 20 years Total Deposits = $120,000

c) How much total interest will you earn?

To find the total interest earned, subtract the total deposits from the final amount:

Total Interest = Final Amount - Total Deposits Total Interest = $183,387 - $120,000 Total Interest = $63,387

So, you will have approximately $183,387 in the account in 20 years, with a total of $120,000 deposited, and you will earn a total of $63,387 in interest.

You deposit $5000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 30 years? $472,303.93

To calculate the future value of regular annual deposits with compound interest, you can use the future value of an annuity formula:

$�=�\frac{(1+�{)}^{�}-1}{�}$

Where:

• $�$ is the future value of the account.
• $�$ is the annual deposit amount ($5,000).
• $�$ is the annual interest rate (7% or 0.07 when expressed as a decimal).
• $�$ is the number of years (30 years in this case).

Now, plug in the values:

$�=5,000$ $�=0.07$ $�=30$

$�=5,000\frac{(1+0.07{)}^{30}-1}{0.07}$

Let's calculate the values step by step:

$�=5,000\frac{(1.07{)}^{30}-1}{0.07}$

Now, calculate the value of $(1.07{)}^{30}$:

$(1.07{)}^{30}\approx 5.427601156$

Finally, calculate the future value:

$�=5,000\frac{5.427601156-1}{0.07}\approx 472,303.93$

So, you will have approximately $472,303.93 in the account in 30 years if you deposit $5,000 each year into an account earning 7% interest compounded annually.

Suppose you want to have $300,000 for retirement in 30 years. Your account earns 6% interest. a) How much would you need to deposit in the account each month? $299 b) How much interest will you earn? $192360

To calculate how much you would need to deposit each month to have $300,000 for retirement in 30 years with an account earning 6% interest, you can use the formula for the future value of regular monthly deposits:

$���=\frac{�\cdot �}{(1+�{)}^{�}-1}$

Where:

• $���$ is the monthly deposit amount (what you want to calculate).
• $�$ is the future value ($300,000).
• $�$ is the monthly interest rate (6% annual interest rate divided by 12 months, so $�=0.06\mathrm{/}12=0.005$).
• $�$ is the number of months (30 years multiplied by 12 months/year, so $�=360$).

Now, plug in the values:

$�=300,000$ $�=0.005$ $�=360$

$���=\frac{300,000\cdot 0.005}{(1+0.005{)}^{360}-1}$

Let's calculate the values step by step:

$���=\frac{1,500}{(1.005{)}^{360}-1}$

Now, calculate the value of $(1.005{)}^{360}$:

$(1.005{)}^{360}\approx 2.712439366$

Finally, calculate the monthly deposit:

$���=\frac{1,500}{2.712439366-1}\approx 299$

a) To have $300,000 for retirement in 30 years with a 6% interest rate, you would need to deposit approximately $299 each month.

b) To calculate the interest earned, subtract the total deposits from the final amount:

Total Interest = Final Amount - Total Deposits Total Interest = $300,000 - ($299 * 360 months) Total Interest = $192,360

b) You will earn approximately $192,360 in interest over the 30-year period.

You have $500,000 saved for retirement. Your account earns 4% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years? $3,029

To calculate how much you can withdraw each month for 20 years with a $500,000 retirement savings account earning 4% interest, you can use the formula for the monthly payment of an annuity:

$���=\frac{��\cdot �}{1-(1+�{)}^{-�}}$

Where:

• $���$ is the monthly withdrawal amount (what you want to calculate).
• $��$ is the present value or the initial amount in the account ($500,000).
• $�$ is the monthly interest rate (4% annual interest rate divided by 12 months, so $�=0.04\mathrm{/}12=0.003333$).
• $�$ is the total number of monthly withdrawals (20 years multiplied by 12 months/year, so $�=240$).

Now, plug in the values:

$��=500,000$ $�=0.003333$ $�=240$

$���=\frac{500,000\cdot 0.003333}{1-(1+0.003333{)}^{-240}}$

Let's calculate the values step by step:

$���=\frac{1,666.67}{1-(1.003333{)}^{-240}}$

Now, calculate the value of $(1.003333{)}^{-240}$:

$(1.003333{)}^{-240}\approx 0.525041305$

Finally, calculate the monthly withdrawal amount:

$���=\frac{1,666.67}{1-0.525041305}\approx 3,029$

So, if you want to be able to take withdrawals for 20 years with a $500,000 retirement savings account earning 4% interest, you can withdraw approximately $3,029 each month to make the money last.

You want to be able to withdraw $45,000 each year for 30 years. Your account earns 7% interest. a) How much do you need in your account at the beginning? $558,406.85 b) How much total money will you pull out of the account? $1,350,000 How much of that money is interest? $791,593.15

To calculate the initial amount you need in your account to withdraw $45,000 each year for 30 years with a 7% interest rate, you can use the present value of an annuity formula:

$��=���\times \frac{1-(1+�{)}^{-�}}{�}$

Where:

• $��$ is the initial amount you need (what you want to calculate).
• $���$ is the annual withdrawal amount ($45,000).
• $�$ is the annual interest rate (7% or 0.07 when expressed as a decimal).
• $�$ is the total number of years (30 years in this case).

Now, plug in the values:

a) Calculate the initial amount you need:

$���=45,000$ $�=0.07$ $�=30$

$��=45,000\times \frac{1-(1+0.07{)}^{-30}}{0.07}$

Let's calculate the values step by step:

$��=45,000\times \frac{1-(1.07{)}^{-30}}{0.07}$

Now, calculate $(1.07{)}^{-30}$:

$(1.07{)}^{-30}\approx 0.1934746768$

Finally, calculate the initial amount needed:

$��=45,000\times \frac{1-0.1934746768}{0.07}\approx 558,406.85$

a) You would need approximately $558,406.85 in your account at the beginning to be able to withdraw $45,000 each year for 30 years with a 7% interest rate.

b) To calculate the total money you will pull out of the account over 30 years, simply multiply the annual withdrawal amount by the number of years:

Total Withdrawals = Annual Withdrawal Amount × Number of Years Total Withdrawals = $45,000 × 30 years = $1,350,000

c) To find the total interest earned, subtract the total withdrawals from the initial amount:

Total Interest = Initial Amount - Total Withdrawals Total Interest = $558,406.85 - $1,350,000 = -$791,593.15 (negative because it represents the interest paid by the account to cover the withdrawals)

So, you would need approximately $558,406.85 in your account at the beginning, you will pull out a total of $1,350,000 over 30 years, and the account will pay approximately $791,593.15 in interest to cover the withdrawals.

You can afford a $1450 per month mortgage payment. You've found a 30 year loan at 8% interest. a) How big of a loan can you afford? $197,611.07 b) How much total money will you pay the loan company? $522,000.00 c) How much of that money is interest? 324,388.93

To calculate the size of the loan you can afford with a $1,450 per month mortgage payment on a 30-year loan at 8% interest, you can use the formula for the present value of an annuity:

$��=���\times \frac{1-(1+�{)}^{-��}}{�}$

Where:

• $��$ is the loan amount you can afford (what you want to calculate).
• $���$ is the monthly payment ($1,450).
• $�$ is the monthly interest rate (8% annual interest rate divided by 12 months, so $�=0.08\mathrm{/}12=0.006666667$).
• $�$ is the total number of months (30 years multiplied by 12 months/year, so $�=360$).

Now, plug in the values:

a) Calculate the loan amount you can afford:

$���=1,450$ $�=0.006666667$ $�=360$

$��=1,450\times \frac{1-(1+0.006666667{)}^{-360}}{0.006666667}$

Let's calculate the values step by step:

$��=1,450\times \frac{1-(1.006666667{)}^{-360}}{0.006666667}$

Now, calculate $(1.006666667{)}^{-360}$:

$(1.006666667{)}^{-360}\approx 0.316919466$

Finally, calculate the loan amount you can afford:

$��=1,450\times \frac{1-0.316919466}{0.006666667}\approx 197,611.07$

a) You can afford a loan of approximately $197,611.07.

b) To calculate the total money you will pay the loan company, multiply the monthly payment by the total number of months:

Total Payments = Monthly Payment × Number of Months Total Payments = $1,450 × 360 months = $522,000

c) To find out how much of that money is interest, subtract the loan amount from the total payments:

Total Interest = Total Payments - Loan Amount Total Interest = $522,000 - $197,611.07 = $324,388.93

So, you can afford a loan of approximately $197,611.07, you will pay a total of $522,000 to the loan company over 30 years, and $324,388.93 of that amount is interest.

You want to buy a $30,000 car. The company is offering a 4% interest rate for 60 months (5 years). What will your monthly payments be? $553

To calculate your monthly car payments for a $30,000 car with a 4% interest rate for 60 months (5 years), you can use the formula for the monthly payment of a fixed-rate loan:

$���=\frac{�\cdot �\cdot (1+�{)}^{�}}{(1+�{)}^{�}-1}$

Where:

• $���$ is the monthly payment (what you want to calculate).
• $�$ is the principal loan amount ($30,000).
• $�$ is the monthly interest rate (4% annual interest rate divided by 12 months, so $�=0.04\mathrm{/}12=0.003333333$).
• $�$ is the total number of months (5 years multiplied by 12 months/year, so $�=60$).

Now, plug in the values:

$�=30,000$ $�=0.003333333$ $�=60$

$���=\frac{30,000\cdot 0.003333333\cdot (1+0.003333333{)}^{60}}{(1+0.003333333{)}^{60}-1}$

Let's calculate the values step by step:

$���=\frac{30,000\cdot 0.003333333\cdot (1.003333333{)}^{60}}{(1.003333333{)}^{60}-1}$

Now, calculate $(1.003333333{)}^{60}$:

$(1.003333333{)}^{60}\approx 1.200277687$

Finally, calculate the monthly payment:

$���=\frac{30,000\cdot 0.003333333\cdot 1.200277687}{1.200277687-1}\approx 553$

So, your monthly car payments for a $30,000 car with a 4% interest rate for 60 months (5 years) will be approximately $553.

You want to buy a $199,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan for the rest. a) How much is the loan amount going to be? $189050 b) What will your monthly payments be if the interest rate is 5%? $1014.86 c) What will your monthly payments be if the interest rate is 6%? $1133.45

Let's break down each part of the question:

a) To calculate the loan amount, you'll start with the total home price and subtract the down payment:

Loan Amount = Total Home Price - Down Payment Loan Amount = $199,000 - (5% of $199,000) Loan Amount = $199,000 - $9,950 Loan Amount = $189,050

So, the loan amount will be $189,050.

b) To calculate the monthly payments for a 30-year loan with a 5% interest rate, you can use the formula for the monthly payment of a fixed-rate loan:

$���=\frac{�\cdot �\cdot (1+�{)}^{�}}{(1+�{)}^{�}-1}$

Where:

• $���$ is the monthly payment (what you want to calculate).
• $�$ is the principal loan amount ($189,050).
• $�$ is the monthly interest rate (5% annual interest rate divided by 12 months, so $�=0.05\mathrm{/}12=0.004166667$).
• $�$ is the total number of months (30 years multiplied by 12 months/year, so $�=360$).

Now, plug in the values:

$�=189,050$ $�=0.004166667$ $�=360$

$���=\frac{189,050\cdot 0.004166667\cdot (1+0.004166667{)}^{360}}{(1+0.004166667{)}^{360}-1}$

Let's calculate the values step by step:

$���=\frac{189,050\cdot 0.004166667\cdot (1.004166667{)}^{360}}{(1.004166667{)}^{360}-1}$

Now, calculate $(1.004166667{)}^{360}$:

$(1.004166667{)}^{360}\approx 1.818403622$

Finally, calculate the monthly payment:

$���=\frac{189,050\cdot 0.004166667\cdot 1.818403622}{1.818403622-1}\approx 1014.86$

So, with a 5% interest rate, your monthly payments will be approximately $1,014.86.

c) To calculate the monthly payments for a 30-year loan with a 6% interest rate, you can use the same formula with the new interest rate:

$���=\frac{�\cdot �\cdot (1+�{)}^{�}}{(1+�{)}^{�}-1}$

Where:

• $�$ is still $189,050.
• $�$ is now the monthly interest rate for 6% (6% annual interest rate divided by 12 months, so $�=0.06\mathrm{/}12=0.005$).

Now, plug in the updated values:

$�=189,050$ $�=0.005$

$���=\frac{189,050\cdot 0.005\cdot (1+0.005{)}^{360}}{(1+0.005{)}^{360}-1}$

Let's calculate the values step by step:

$���=\frac{189,050\cdot 0.005\cdot (1.005{)}^{360}}{(1.005{)}^{360}-1}$

Now, calculate $(1.005{)}^{360}$:

$(1.005{)}^{360}\approx 1.966224606$

Finally, calculate the monthly payment:

$���=\frac{189,050\cdot 0.005\cdot 1.966224606}{1.966224606-1}\approx 1133.45$

So, with a 6% interest rate, your monthly payments will be approximately $1,133.45.

You deposit $6000 in an account earning 8% interest compounded monthly. How much will you have in the account in 15 years? $19841.5

To calculate how much money you will have in the account in 15 years when you deposit $6,000 with an 8% annual interest rate compounded monthly, you can use the formula for compound interest:

$�=�{(1+\frac{�}{�})}^{��}$

Where:

• $�$ is the future amount of money in the account.
• $�$ is the initial principal amount ($6,000).
• $�$ is the annual interest rate (8% or 0.08 when expressed as a decimal).
• $�$ is the number of times interest is compounded per year (monthly, so $�=12$).
• $�$ is the number of years the money is invested or saved (15 years in this case).

Now, plug in the values and calculate:

$�=6,000$ $�=0.08$ $�=12$ $�=15$

$�=6,000{(1+\frac{0.08}{12})}^{12\cdot 15}$

Let's calculate the values step by step:

$�=6,000{(1+\frac{0.08}{12})}^{12\cdot 15}$

Now, calculate the value of $(1+\frac{0.08}{12}{)}^{12\cdot 15}$:

$(1+\frac{0.08}{12}{)}^{12\cdot 15}\approx 3.3089012909$

Finally, multiply this value by the initial principal amount:

$�\approx 6,000\times 3.3089012909\approx 19,841.5$

So, if you deposit $6,000 in an account earning 8% interest compounded monthly, you will have approximately $19,841.5 in the account in 15 years.

You deposit $4000 in an account earning 3% interest compounded monthly. How much will you have in the account in 10 years? $5396

To calculate how much money you will have in the account in 10 years when you deposit $4,000 with a 3% annual interest rate compounded monthly, you can use the formula for compound interest:

$�=�{(1+\frac{�}{�})}^{��}$

Where:

• $�$ is the future amount of money in the account.
• $�$ is the initial principal amount ($4,000).
• $�$ is the annual interest rate (3% or 0.03 when expressed as a decimal).
• $�$ is the number of times interest is compounded per year (monthly, so $�=12$).
• $�$ is the number of years the money is invested or saved (10 years in this case).

Now, plug in the values and calculate:

$�=4,000$ $�=0.03$ $�=12$ $�=10$

$�=4,000{(1+\frac{0.03}{12})}^{12\cdot 10}$

Let's calculate the values step by step:

$�=4,000{(1+\frac{0.03}{12})}^{12\cdot 10}$

Now, calculate the value of ${(1+\frac{0.03}{12})}^{12\cdot 10}$:

${(1+\frac{0.03}{12})}^{12\cdot 10}\approx 1.3498588076$

Finally, multiply this value by the initial principal amount:

$�\approx 4,000\times 1.3498588076\approx 5,398.63$

So, if you deposit $4,000 in an account earning 3% interest compounded monthly, you will have approximately $5,398.63 in the account in 10 years.

Find the simple interest owed if $870 is borrowed at 7.3% for 9 years. $571.59

To find the simple interest owed when borrowing $870 at a 7.3% interest rate for 9 years, you can use the simple interest formula:

$�=�\cdot �\cdot �$

Where:

• $�$ is the interest.
• $�$ is the principal amount borrowed ($870).
• $�$ is the annual interest rate (7.3% or 0.073 when expressed as a decimal).
• $�$ is the time the money is borrowed for (9 years).

Now, plug in the values:

$�=870$ $�=0.073$ $�=9$

$�=870\cdot 0.073\cdot 9$

Let's calculate the interest:

$�=870\cdot 0.073\cdot 9$ $�=570.87$

So, the simple interest owed when borrowing $870 at a 7.3% interest rate for 9 years is approximately $571.59.

How much should you invest at 4% simple interest in order to earn $50 interest in 13 months?

$1,153.85

To calculate how much you should invest at a 4% simple interest rate to earn $50 in interest over 13 months, you can use the simple interest formula:

$�=�\cdot �\cdot �$

Where:

• $�$ is the interest earned ($50).
• $�$ is the principal amount (what you want to calculate).
• $�$ is the annual interest rate (4% or 0.04 when expressed as a decimal).
• $�$ is the time the money is invested for, in years (13 months converted to years is $13\mathrm{/}12$ or approximately 1.0833 years).

Now, plug in the values:

$�=50$ $�=0.04$ $�=1.0833$

We want to solve for $�$, so rearrange the formula:

$�=\frac{�}{�\cdot �}$

Now, plug in the values and calculate:

$�=\frac{50}{0.04\cdot 1.0833}$

Let's calculate it:

$�=\frac{50}{0.043332}$ $�\approx 1,153.85$

So, you should invest approximately $1,153.85 at a 4% simple interest rate to earn $50 in interest over 13 months.

What is the simple interest rate on a $2450 investment paying $1,024.10 interest in 19 years? 2.2% (round to the nearest tenth of a percent)

To find the simple interest rate on a $2,450 investment that pays $1,024.10 in interest over 19 years, you can use the simple interest formula:

$�=�\cdot �\cdot �$

Where:

• $�$ is the interest earned ($1,024.10).
• $�$ is the principal amount ($2,450).
• $�$ is the annual interest rate (what you want to calculate).
• $�$ is the time the money is invested for (19 years).

Now, plug in the values:

$�=1,024.10$ $�=2,450$ $�=19$

We want to solve for $�$, so rearrange the formula:

$�=\frac{�}{�\cdot �}$

Now, plug in the values and calculate:

$�=\frac{1,024.10}{2,450\cdot 19}$

Let's calculate it:

$�=\frac{1,024.10}{46,550}$

Now, divide to find $�$:

$�\approx 0.02199$

To round to the nearest tenth of a percent, we can multiply by 100:

$�\approx 2.2\mathrm{\%}$

So, the simple interest rate on a $2,450 investment that pays $1,024.10 in interest over 19 years is approximately 2.2%.

You deposit $1600 in a savings account paying 4% simple interest. How much interest will you earn in 5 years? 320 How much is in the account at the end of 5 years? 1920

To calculate the interest earned and the total amount in the account at the end of 5 years for a $1,600 deposit in a savings account paying 4% simple interest, you can use the simple interest formula:

$�=�\cdot �\cdot �$

Where:

• $�$ is the interest earned.
• $�$ is the principal amount ($1,600).
• $�$ is the annual interest rate (4% or 0.04 when expressed as a decimal).
• $�$ is the time the money is invested for (5 years).

Now, plug in the values:

$�=1,600$ $�=0.04$ $�=5$

a) Calculate the interest earned:

$�=1,600\cdot 0.04\cdot 5$

Let's calculate it:

$�=1,600\cdot 0.04\cdot 5=320$

So, you will earn $320 in interest over 5 years.

b) To find the total amount in the account at the end of 5 years, add the interest to the principal:

Total Amount = Principal + Interest Total Amount = $1,600 + $320 = $1,920

So, you will have $1,920 in the account at the end of 5 years.

A friend lends you $900, which you agree to repay with 4% interest. How much will you have to repay? $936 How much of that was interest? $36

To calculate how much you will have to repay and how much of that is interest when you borrow $900 with a 4% interest rate, you can use the formula for calculating interest:

$��������=���������\times ����$

Where:

• $��������$ is the interest amount.
• $���������$ is the initial borrowed amount ($900).
• $����$ is the interest rate (4% or 0.04 when expressed as a decimal).

a) Calculate the interest amount:

Interest = $900 \times 0.04 = $36

b) To find the total amount you will have to repay, simply add the interest to the principal:

Total Repayment = Principal + Interest Total Repayment = $900 + $36 = $936

So, you will have to repay a total of $936, and $36 of that amount is interest.

A friend lends you $380, which you agree to repay with 6% interest. How much will you have to repay? $402.80

To calculate how much you will have to repay when borrowing $380 with a 6% interest rate, you can use the formula for calculating the total repayment:

Total Repayment = Principal + Interest

Where:

• Principal is the initial borrowed amount ($380).
• Interest is the interest amount, which can be calculated using the formula: Interest = Principal × Rate.

Now, let's calculate the interest amount:

Interest = $380 × 0.06 (6% expressed as a decimal) = $22.80

Now, add the interest to the principal to find the total repayment:

Total Repayment = $380 + $22.80 = $402.80

So, you will have to repay a total of $402.80, which includes the $380 principal amount and $22.80 in interest.

The city is issuing bonds to raise money for a building project. You obtain a $3200 bond that pays 3% interest annually that matures in 5 years. How much interest will you earn? $480

To calculate the interest earned on a bond, you can use the formula for simple interest:

$�=�\cdot �\cdot �$

Where:

• $�$ is the interest earned.
• $�$ is the principal amount (the face value of the bond, $3200 in this case).
• $�$ is the annual interest rate (3% or 0.03 when expressed as a decimal).
• $�$ is the time the money is invested (in years, 5 years in this case).

Now, plug in the values:

$�=3200\cdot 0.03\cdot 5$

Let's calculate it:

$�=3200\cdot 0.03\cdot 5=480$

So, you will earn $480 in interest over the 5-year period.

Skills Quiz - Unit 7 Finance:

You deposit $5000 in an account earning 8% interest compounded monthly. How much will you have in the account in 5 years? $7,449.23

To calculate how much money you will have in the account in 5 years when you deposit $5,000 with an 8% annual interest rate compounded monthly, you can use the formula for compound interest:

$�=�{(1+\frac{�}{�})}^{��}$

Where:

• $�$ is the future amount of money in the account.
• $�$ is the principal amount ($5,000).
• $�$ is the annual interest rate (8% or 0.08 when expressed as a decimal).
• $�$ is the number of times interest is compounded per year (monthly, so $�=12$).
• $�$ is the number of years the money is invested or saved (5 years in this case).

Now, plug in the values:

$�=5,000$ $�=0.08$ $�=12$ $�=5$

$�=5,000{(1+\frac{0.08}{12})}^{12\cdot 5}$

Let's calculate the values step by step:

$�=5,000{(1+\frac{0.08}{12})}^{12\cdot 5}$

Now, calculate the value of ${(1+\frac{0.08}{12})}^{12\cdot 5}$:

${(1+\frac{0.08}{12})}^{12\cdot 5}\approx 1.469058107$

Finally, multiply this value by the initial principal amount:

$�\approx 5,000\times 1.469058107\approx 7,345.29$

So, if you deposit $5,000 in an account earning 8% interest compounded monthly, you will have approximately $7,345.29 in the account in 5 years.

You can afford a $350 per month car payment. You've found a 4 year loan at 4% interest. How big of a loan can you afford? $15498.4068

To calculate how big of a car loan you can afford with a $350 per month car payment on a 4-year loan at 4% interest, you can use the formula for the present value of an annuity:

$��=���\times \frac{1-(1+�{)}^{-��}}{�}$

Where:

• $��$ is the maximum loan amount you can afford (what you want to calculate).
• $���$ is the monthly payment ($350).
• $�$ is the monthly interest rate (4% annual interest rate divided by 12 months, so $�=0.04\mathrm{/}12=0.003333333$).
• $�$ is the total number of months (4 years multiplied by 12 months/year, so $�=48$).

Now, plug in the values:

$���=350$ $�=0.003333333$ $�=48$

$��=350\times \frac{1-(1+0.003333333{)}^{-48}}{0.003333333}$

Let's calculate the values step by step:

$��=350\times \frac{1-(1.003333333{)}^{-48}}{0.003333333}$

Now, calculate $(1.003333333{)}^{-48}$:

$(1.003333333{)}^{-48}\approx 0.864139424$

Finally, calculate the maximum loan amount you can afford:

$��\approx 350\times \frac{1-0.864139424}{0.003333333}\approx 15,498.4068$

So, you can afford a car loan of approximately $15,498.41.

You have $500,000 saved for retirement. Your account earns 5% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 15 years? $3953.97

To calculate the monthly withdrawal amount you can take from your retirement savings of $500,000, given a 5% annual interest rate, such that it lasts for 15 years, you can use the formula for the monthly payment of an annuity:

$���=\frac{�\cdot �}{1-(1+�{)}^{-��}}$

Where:

• $���$ is the monthly withdrawal amount (what you want to calculate).
• $�$ is the initial savings or principal amount ($500,000).
• $�$ is the monthly interest rate (5% annual interest rate divided by 12 months, so $�=0.05\mathrm{/}12=0.004166667$).
• $�$ is the total number of months in 15 years (15 years multiplied by 12 months/year, so $�=180$).
• $�$ is the total number of years you want the withdrawals to last (15 years).

Now, plug in the values:

$�=500,000$ $�=0.004166667$ $�=180$ $�=15$

$���=\frac{500,000\cdot 0.004166667}{1-(1+0.004166667{)}^{-180}}$

Let's calculate the values step by step:

$���=\frac{500,000\cdot 0.004166667}{1-(1.004166667{)}^{-180}}$

Now, calculate $(1.004166667{)}^{-180}$:

$(1.004166667{)}^{-180}\approx 0.635518081$

Finally, calculate the monthly withdrawal amount:

$���\approx \frac{500,000\cdot 0.004166667}{1-0.635518081}\approx 3,953.97$

So, you can withdraw approximately $3,953.97 each month from your retirement savings of $500,000, and it will last for 15 years with a 5% interest rate.

Suppose you want to have $500,000 for retirement in 25 years. Your account earns 10% interest. How much would you need to deposit in the account each month? $376.84

To calculate how much you would need to deposit in an account each month to have $500,000 for retirement in 25 years with a 10% annual interest rate, you can use the formula for the monthly payment of an annuity:

$���=\frac{�\cdot �}{1-(1+�{)}^{-��}}$

Where:

• $���$ is the monthly deposit amount (what you want to calculate).
• $�$ is the future value or target amount ($500,000).
• $�$ is the monthly interest rate (10% annual interest rate divided by 12 months, so $�=0.10\mathrm{/}12=0.008333333$).
• $�$ is the total number of months in 25 years (25 years multiplied by 12 months/year, so $�=300$).
• $�$ is the total number of years (25 years).

Now, plug in the values:

$�=500,000$ $�=0.008333333$ $�=300$ $�=25$

$���=\frac{500,000\cdot 0.008333333}{1-(1+0.008333333{)}^{-300}}$

Let's calculate the values step by step:

$���=\frac{500,000\cdot 0.008333333}{1-(1.008333333{)}^{-300}}$

Now, calculate $(1.008333333{)}^{-300}$:

$(1.008333333{)}^{-300}\approx 0.148734528$

Finally, calculate the monthly deposit amount:

$���\approx \frac{500,000\cdot 0.008333333}{1-0.148734528}\approx 376.84$

So, you would need to deposit approximately $376.84 in the account each month to have $500,000 for retirement in 25 years with a 10% interest rate.

You have $2,000 on a credit card that charges a 12% interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)? $44.49 each month

To calculate how much you need to pay each month to pay off a $2,000 credit card debt with a 12% annual interest rate in 5 years, you can use the formula for the monthly payment of an amortizing loan:

$���=\frac{�\cdot �}{1-(1+�{)}^{-��}}$

Where:

• $���$ is the monthly payment (what you want to calculate).
• $�$ is the initial debt amount ($2,000).
• $�$ is the monthly interest rate (12% annual interest rate divided by 12 months, so $�=0.12\mathrm{/}12=0.01$).
• $�$ is the total number of times that interest is compounded per year (12 for monthly payments).
• $�$ is the total number of years (5 years).

Now, plug in the values:

$�=2,000$ $�=0.01$ $�=12$ $�=5$

$���=\frac{2,000\cdot 0.01}{1-(1+0.01{)}^{-12\cdot 5}}$

Let's calculate the values step by step:

$���=\frac{2,000\cdot 0.01}{1-(1.01{)}^{-60}}$

Now, calculate $(1.01{)}^{-60}$:

$(1.01{)}^{-60}\approx 0.547029478$

Finally, calculate the monthly payment:

$���\approx \frac{20}{1-0.547029478}\approx 44.49$

So, you would need to pay approximately $44.49 each month to pay off the $2,000 credit card debt with a 12% annual interest rate in 5 years, assuming you don't charge anything new to the card.

How much should you invest at 2.3% simple interest in order to earn $55 interest in 15 months? $1,913.04

Let's calculate the correct amount you should invest at a 2.3% simple interest rate to earn $55 in interest over 15 months:

We can use the simple interest formula:

$�=�\cdot �\cdot �$

Where:

• $�$ is the interest earned ($55).
• $�$ is the principal amount (what you want to calculate).
• $�$ is the annual interest rate (2.3% or 0.023 when expressed as a decimal).
• $�$ is the time the money is invested for (15 months converted to years is $15\mathrm{/}12$ or 1.25 years).

Now, plug in the values:

$�=55$ $�=0.023$ $�=1.25$

We want to solve for $�$, so rearrange the formula:

$�=\frac{�}{�\cdot �}$

Now, plug in the values and calculate:

$�=\frac{55}{0.023\cdot 1.25}$

Let's calculate it:

$�=\frac{55}{0.02875}$

Now, divide to find $�$:

$�\approx 1,913.04$

So, you should invest approximately $1,913.04 at a 2.3% simple interest rate to earn $55 in interest over 15 months.

What is the simple interest rate on a $1150 investment paying $485.76 interest in 8.8 years? 4.8% (rounded to the nearest tenth of a percent)

To calculate the simple interest rate on a $1,150 investment that pays $485.76 in interest over 8.8 years, you can use the formula for simple interest:

$�=�\cdot �\cdot �$

Where:

• $�$ is the interest earned ($485.76).
• $�$ is the principal amount ($1,150).
• $�$ is the annual interest rate (what you want to calculate).
• $�$ is the time the money is invested for (8.8 years).

Now, plug in the values:

$�=485.76$ $�=1,150$ $�=8.8$

We want to solve for $�$, so rearrange the formula:

$�=\frac{�}{�\cdot �}$

Now, plug in the values and calculate:

$�=\frac{485.76}{1,150\cdot 8.8}$

Let's calculate it:

$�=\frac{485.76}{10,120}$

Now, divide to find $�$:

$�\approx 0.0479$

To round to the nearest tenth of a percent, we can multiply by 100:

$�\approx 4.79\mathrm{\%}$

So, the simple interest rate on a $1,150 investment that pays $485.76 in interest over 8.8 years is approximately 4.8%.

You deposit $1690 in a savings account paying 3.9% simple interest. How much interest will you earn in 2 years? 131.82 How much is in the account at the end of 2 years? 1821.82

To calculate the correct future value of your deposits, compounded annually, you can use the formula for the future value of an annuity with compound interest:

$��=�\cdot \frac{(1+�{)}^{�}-1}{�}$

Where:

• $��$ is the future value of the annuity (the amount you want to calculate).
• $�$ is the annual deposit amount ($2,000).
• $�$ is the annual interest rate (2% or 0.02 when expressed as a decimal).
• $�$ is the number of years (20 years in this case).

Now, plug in the values:

$�=2,000$ $�=0.02$ $�=20$

$��=2,000\cdot \frac{(1+0.02{)}^{20}-1}{0.02}$

Let's calculate the values step by step:

$��=2,000\cdot \frac{(1.02{)}^{20}-1}{0.02}$

Now, calculate $(1.02{)}^{20}$:

$(1.02{)}^{20}\approx 1.48594606$

Now, calculate the future value:

$��=2,000\cdot \frac{1.48594606-1}{0.02}$

Now, subtract 1 from 1.48594606:

$��=2,000\cdot \frac{0.48594606}{0.02}$

Now, divide to find the future value:

$��\approx 2,000\cdot 24.297303$

$��\approx 48,594.60$

So, you will have approximately $48,594.60 in the account in 20 years if you deposit $2,000 each year into an account earning 2% interest compounded annually.

In 2014, the median salary nationwide for a high school teacher was $56,310 per year. The median annual wage for all workers was $35,540. SOURCE: United States. Department of Labor. "High School Teachers." Occupational Outlook Handbook. 17 Dec. 2015. Web. 7 March 2016. Suppose a worker makes $25,000 in wages per year. Find the percent increase in salary the worker can expect if he/she trains to be a teacher and can expect to earn a salary of $42,000. Enter your response to the nearest 0.1% 68%

To find the percent increase in salary when a worker transitions from making $25,000 per year to earning a salary of $42,000 as a teacher, you can use the following formula:

$\text{Percent Increase}=\frac{\text{New Salary}-\text{Old Salary}}{\text{Old Salary}}\times 100$

Where:

• Old Salary is the initial salary ($25,000).
• New Salary is the final salary as a teacher ($42,000).

Now, plug in the values:

$\text{Percent Increase}=\frac{42,000-25,000}{25,000}\times 100$

Calculate the numerator:

$\text{Percent Increase}=\frac{17,000}{25,000}\times 100$

Now, divide to find the percent increase:

$\text{Percent Increase}=\frac{17}{25}\times 100\approx 68\mathrm{\%}$

So, the worker can expect a salary increase of approximately 68% when transitioning to become a teacher with a salary of $42,000 per year.

Project # 7 Statistical Graphs(B)

1. The stacked bar chart below shows the composition of religious affiliation of incoming refugees to the United States for the months of February-June 2017.

a. Compare the percent of Christian, Muslim, Other and Unaffiliated refugees to the U.S during this time period. Write at least 3 sentences in your response.

Christian religion has grown the most compared to the other religions. Muslim grew the second most quickly. Other religions grew some but then decreased during June. And people that aren’t affiliated didn’t grow at all. 

b. Suppose the number of refugee arrivals for these months of Feb. 2017 to June 2017 are as follows: 

i. 4,080 for February,  

ii. 2,670 for March,  

iii. 3,916 for April,  

iv. 3,189 for May, 

v. 2,146 for June. 

c. Using these numbers, calculate how many refugees (round to the nearest whole person) 

i. In May are Muslim, Christian, Other, Unaffiliated.

Number of Christians = 57/100 x 2,146 =1223.22  rounded to 1223

Number of Muslims= 29/100 x 2146= 622.34 rounded to 622

Number of Other= 13/100 x 2146= 278.98 rounded to 279

Number of Unaffiliated= 1/100 x 2146=21.46 rounded to 22

ii. In June are Muslim, Christian, Other, Unaffiliated.

Number of Christians = 57/100 x 2,146 =1223.22  rounded to 1223

Number of Muslim= 31/100 x 2146=665.26 rounded to 665

Number of other= 11/100 x 2146=236.06 rounded to 236

                              Number of Unaffiliated= 1/100 x 2146=21.46 rounded to 22

 Must show calculations/formula for credit. Any answer given with no calculations shown will result in no credit for that answer. 

Use this chart to answer question 1a and 1c

2. The bar chart below shows the number of refugees entering the US from Jan. 21 to June 30, 2017 by nationality. The top 10 nationalities are shown in the chart.

a. Summarize what you see in this chart in at least 3 sentences.

The total number of people entering from the top 10 countries are 17001. The top 3 countries of these countries are Democratic Republic of Congo, Iraq, and Burma. Refugees from Africa is in the top ten. The countries that are 6447 in number is from Democratic Republic of Congo, Somalia and Eritrea. Refugees from Asia in the top 10 countries are 8450.

b. Suppose during this time 17001 refugees were admitted to the United States. What percentage (to the nearest 10th percent) of refugees come from each of these 

countries? Must show calculations/formula for credit. Any answer given with no calculations shown will result in no credit for that answer. 

Total Refugees= 17001

Refugees of a country = (refugee from that country / total refugees) *100

El Salvador= (501/ 17001)*100 =2.9468 rounded 3.0%

Iran = (897/17001) *100=5.276 rounded 5.28%

Eritrea =(1333/17001) * 100=7.840 rounded 7.84% 

Bhutan =(1381/17001) * 100 = 8.123 rounded 8.12%

Ukraine =(1603/ 17001) *100= 9.428 rounded 9.43%

Syria =( 1779 / 17001) * 100=10.464 rounded 10.46 

Somalia= (1879/ 17001) * 100 =11.052 rounded 11.05% 

Iraq =(1923/ 17001) * 100 = 11.311 rounded 11.31%

Burma =( 2470/ 17001) * 100 =14.528 rounded 14.53% 

Demo Republic of Congo = (3235/ 17001) * 100= 19.028 rounded 19.03%

Use this chart to answer question 2a and 2b

3. The bar chart below shows the top 10 states where refugees are resettled from fiscal years of 2002 to 2017.

a. Summarize what you see in this chart in at least 3 sentences.

The chart shows the number of refugees in thousands between Oct 1st 2002 and Sept 2017 that settled in the states of California, New York, Texas, Florida, Arizona, Minnesota, Washington, Michigan, Georgia, and Pennsylvania. The highest number of settlement in the state of California and the lowest in Pennsylvania. The mean and median of the number of refugees resetting between Oct 1st, 2002 and Sept 2017 who settled in the states are 52.3 thousand and 42 thousand respectively with a range of 72 thousand. The standard deviation is 22.35 thousand which means moderately values of most of the refugee resettlement values are below 42 thousand. 50% of the refugee resettlement values are below 42 thousand. We see a positive bias in the data.  

b. Suppose there were 523,000 refugee arrivals during this time period. Calculate the percentage of refugees (to the nearest 10th percent) resettled into each of these top 10 resettlement states. Must show calculations/formula for credit. Any answer given with no calculations shown will result in no credit for that answer. 

California :(105/523)*100= 20.076 rounded to 20.08%

Texas :(84/523)*100= 16.061 rounded to 16.06%

New York :(55/523)*100= 10.516 rounded to 10.52%

Florida :(47/523)*100= 8.986 rounded to 8.99%

Washington :(42/523)*100= 8.030 rounded to 8.03%

Minnesota :(42/523)*100= 8.030 rounded to 8.03%

Arizona :(40/523)*100= 7.648 rounded to 7.65%

Michigan :(39/523)*100= 7.456 rounded to 7.46%

Georgia :(36/523)*100= 6.883 rounded to 6.88%

Pennsylvania :(33/523)*100= 6.309 rounded to 6.31%

Use this chart to answer question 3a and 3b

Use this chart to answer questions 4a and 4b

4.

4a 

What conclusions can you draw from these graphs? Write at least 3 sentences in your response.

We can conclude that the number of refugees admitted is more in the Middle East, Asia-Pacific and Africa as compared to Europe and America. We can also conclude that the number of refugees admitted in the Middle East, Africa and Asia-Pacific is less in the beginning of the year and increases in the ending year. In Europe the number of refugees admitted is more in the beginning of the year and decreases in the ending year. America doesn’t change. 

4b

Calculate the absolute change and relative change (to nearest tenth percent) for refugees admitted to the US from the Middle East. Interpret these values in a  sentence. Must show calculations/formula for credit. Any answer given with no calculations shown will result in no credit for that answer. 

For South Africa Africa:

Absolute change=20000 - 3000 = 17000

Relative change (20000 - 3000)/3000 = 17000/3000 = 5.67

From absolute change we can tell the number of refugees admitted has increased by 17000 and that there is a relative change increased by 5.67%

For Middle East:

Absolute change = 16000-2000 = 14000

Relative change = (16000-2000) / 2000 =14000 / 2000 = 7

From the absolute change we can tell the number of refugees admitted has increased by 14000 and there is a relative change increased by 7%

For Asia-Pacific:

Absolute change = 11000 - 6000 = 5000

Relative change = (11000 - 6000) / 6000 = 5000 / 6000 = 0.83

For the absolute change we can tell the number of refugees admitted has increased by 5000 and there is a relative change increased by 0.83%

                             For Europe:

                             Absolute change = 5000 - 15000 = -10000

                             Relative change = (5000-15000) / 15000 = -10000 / 15000 = -0.67  

 has decreased       by 5000 and there is a relative change increased by 0.83%   

                             by 10000 and there is a relative change decreased by 0.67%    

                             

                             For America:   

                             Absolute change = 2000 - 2000 = 0

                             Relative change = (2000 - 2000) / 2000 = 0 / 2000 = 0    

                             For the absolute change we can tell that there is no change in the number of 

                             refugees admitted and the relative change has no change as well.                                          

5. Summarize what you see in the prior graph (number of refugees each fiscal year admitted into the US by region of nationality) and summarize what you see in the below graph (Number of refugee arrivals each year into the US/Global refugee population).

a. What do the two graphs together convey? Write your answer in at least 3 sentences.

The graph that is given is an example of a line graph. We have a graph that shows the number of refugee arrivals into the US in thousands over the years 1985 to 2015. The number of refugees was high in 1990 and 2010. In the remaining years the number of refugees coming to the us was in a range of 55 to 60 thousand. 

Use this to answer questions 5a and 5b

b. Find the absolute and relative change (to the nearest tenth percent) for the number of refugee arrivals into the US from 1990 to 2015. Interpret these numbers in a sentence. Must show calculations/formula for credit. Any answer given with no calculations shown will result in no credit for that answer.

                                     number of refugee arrival into us in 2010 = 80 thousands

                                     number of refugee arrival into us in 1985 = 54 thousands

                                     absolute change= number of refugee arrival into us in 2010 - number of refugee  

                                     arrival into us in 1985                                                                           

                                     absolute change= 80-54

                                     absolute change=26%

                                     relative change= (absolute change/number of refugee arrival in 2010) x 100

                                     number of refugee arrival in 2010=80

                                     relative change = 26/80x100= 32.5%