Question

1.An investment will pay you $500 every year starting 1 year from today and goes on forever. If the interest rate is 5% p.a., what is the maximum price that you would pay for this investment?

2.You are given $200 each year starting next year and finishing in 15 years (t=15). If the interest rate is 6% p.a., what is the maximum price that you would pay for these cash flows?

3.You borrow $100,000 today, the annual interest rate is 12%, you repay the interest and principle once a year. The loan will be payoff in 30 years. What is your annual payment?

4.Matt plans to make 35 equal yearly deposits into his retirement account starting one year from now (t=1). Starting at t=36, he will make 20 equal withdrawals of $150,000 each year from this account. The interest rate is 7% p.a. How much must Matt deposit each year to satisfy his retirement needs?

5.Kevin is planning on saving for retirement. He wishes to have $500,000 in his retirement account in 40 years (t=40). He plans on doing this by making equal yearly deposits into his savings account starting from t=1. The interest rate is 4% p.a. How much does he need to deposit each year? (20 points)

Answer 1

Answer 1.

First payment = $500
Interest rate = 5%

Present value = First payment / Interest rate
Present value = $500 / 0.05
Present value = $10,000

Maximum price paid for these cash flows is $10,000

Answer 2.

Annual payment = $200
Interest rate = 6%
Period = 15 years

Present value = $200/1.06 + $200/1.06^2 + .... + $200/1.06^15
Present value = $200 * (1 - (1/1.06)^15) / 0.06
Present value = $1,942.45

Maximum price paid for these cash flows is $1,942.45