Question

1.

You’d like to buy a small ranch when you retire in 37 years. You estimate that in 37 years you’ll need $9 million to do so. If you can earn 1.0% per month, how much will you need to invest each month (for 37 years), starting next month, in order to reach your goal? Round to the nearest cent.

2.

Suppose the Dutch Water Authority offered to sell you a perpetuity of $157 per year, every year, forever starting next year. If the appropriate discount rate is 4.9%, what would you be willing to pay today for the perpetuity? Round to the nearest cent.

Answer 1

(1) Savings Tenure = 37 years or (37 x 12) = 444 months, Target Future Value = $ 9 million, Interest Rate = 1% per month

Let the required monthly deposits be $ k

Therefore, 9000000 = k x (1.01)^(443) + k x (1.01)^(442) +.................+ k = [{(1.01)^(444) - 1} / {1.01-1}] x k = k x 8192.58553

k = 9000000 / 8912.58553 = $ 1098.55

(2) Annual Perpetuity = $ 157, Discount Rate = 4%

Fair Price of Perpetuity = PV of Perpetuity = 157 / 0.04 = $ 3925