1) Funding your retirement You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $20,000 at the end of each year for the 30 years between retirement and death (a psychic told you that you would die exactly 30 years after you retire). You know that you will be able to earn 11% per year during the 30-year retirement period.

a. How large a fund will you need when you retire in 20 years to provide the 30-year, $20,000 retirement annuity?

b. How much will you need today as a single amount to provide the fund calculated in part a if you earn only 9% per year during the 20 years preceding retirement?

c. What effect would an increase in the rate you can earn both during and prior to retirement have on the values found in parts a and b? Explain.

d. Now assume that you will earn 10% from now through the end of your retirement. You want to make 20 end-of-year deposits into your retirement account that will fund the 30-year stream of $20,000 annual annuity payments. How large do your annual deposits have to be?

2) Monthly loan payments Tim Smith is shopping for a used car. He has found one priced at $4,500. The dealer has told Tim that if he can come up with a down payment of $500, the dealer will finance the balance of the price at a 12% annual rate over 2 years (24 months).

a. Assuming that Tim accepts the dealer’s offer, what will his monthly (end-of-month) payment amount be?

b. Use a financial calculator or spreadsheet to help you figure out what Tim’s monthly payment would be if the dealer were willing to finance the balance of the car price at a 9% annual rate.