Allocating Resources over Time

1. If you invest $100 today at an interest rate of 7% a year, how much would you have 10 years from now, assuming no withdrawals from the interim?

2. What is the effective annual rates of 9% APR compounded monthly?

3. John receives a $1,000 bonus. He plans to invest in a savings account that earns annual interest rate of 8%. Using the rule of 72, approximately how long will it take for John to increase his wealth to $2,000?

4. You win a $500,000 lottery, which pays 20,000 per year for 25 years. How much is the prize really worth, i.e. the present value of the lottery, assuming an interest rate of 7% a year?

5. Your cousin has asked for your advice on whether or not to buy a bond for $1000, which will make one payment of $1,300 four years from now, or invest in the local bank account that pays 6% a year.

a) What is the internal rate of return on the bond’s cash flows?

b) Would you advise your cousin to purchase this bond or to invest in the local bank account? Justify your answer

6. You are taking out a $120,000 mortgage loan to be repaid over 30 years in 360 monthly payments.

a) If interest rate is 12% a year, what is the amount of monthly payments?

b) If you can only afford to pay $1,000 per month, how large a loan could you take?

7. You are trying to decide whether to (1) buy a car for 4.0% APR for the full $25,000 purchase price over three years, or (2) receive $2,000 cash back and finance the rest at the bank rate of 8.0%. Both loans have monthly payments over three years.

a) What is the monthly payment from buying a car at full price at 4.0% APR (option 1)?

b) After receiving the cash rebate, what is the monthly payment from a bank loan at 12.0% APR (option 2)?

c) Which option would you choose? Briefly explain.