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# Assorted problems in Finance

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1. Jane Alexander currently has \$,7,750 in a money market account paying 7.25% annually. She plans to use this amount and her savings over the next 5 years to make a down payment on a house. She estimates that she will need \$20,000 in 5 years. How much should she invest in the money market account semi-annually over the next 5 years to achieve this target?

2. You are the manager of an annuity settlement company. Jim Patton just won the state lottery which promises to pay him \$1,000 per year for 20 years, starting from today, and \$2,000 per year for years 21-45, given a 9% discount rate. Your company wants to purchase the proceeds from the lottery from Jim. What is the most that your company can offer?

3. Aquaman stock has exhibited a standard deviation in returns of 0.7, whereas Green Lantern stock has exhibited a standard deviation of 0.8. The correlation coefficient between the stock returns is 0.1. What is the standard deviation of a portfolio composed of 70% Aquaman and 30% Green Lantern?

4. The stocks of Microsoft and Apple have a correlation coefficient of 0.6. The variance of Microsoft stock is 0.4 and the variance of Apple stock is 0.3. What is the covariance between the two stocks?

#### Solution Preview

1. Jane Alexander currently has \$,7,750 in a money market account paying 7.25% annually. She plans to use this amount and her savings over the next 5 years to make a down payment on a house. She estimates that she will need \$20,000 in 5 years. How much should she invest in the money market account semi-annually over the next 5 years to achieve this target?

Let Jane deposits R amount per semiannually.
Current accumulation=C=\$7750
Rate of interest=i=7.25%
Number of periods=n=5*2=10
Total Future value=FV=\$20000

FV=C*(1+i)^n+ R*((1+i)^n-1)/i
20000=7750*(1+7.25%)^10+R*((1+7.25%)^10-1)/7.25%=15605.39+13.98068R ...

#### Solution Summary

There are 4 problems related to topics in finance. Solutions to first two problems depict the methodology to estimate the current value of investment/settlement. Solutions to last two problems describe the steps to calculate standard deviation of portfolio and covariance between the two given stocks. Calculations are carried out with the help of suitable formulas.

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