Question

4)

A) Suppose you want to be able to withdraw $1,200 per month at the end of each month for the next year. You can earn 6% per year (compounding monthly) on the amount you invest today. How much must you deposit today to be able to make the planned withdrawals over the next year?

B) Suppose you fall on hard times and need to get a payday loan. The terms of the loan are that you write a check to PAYDAY inc for $120 that is postdated 10 days from now and they’ll give you $100 today. What is the Effective Yield (in decimal form)?

C)Suppose you are looking to begin investing $500 a month into an account that pays 13.5% per year (end of month payments). If you are currently 25 years old and plan to retire in 40 years, what will this account be worth upon retirement?

Answer 1

(A) Monthly Withdrawals = $ 1200 (end of month) to begin a year and a month from now, Interest Rate = 6 % compounded monthly, Number of Withdrawals = 12

Monthly Rate = 6/12 = 0.5 %

Total Present Value of All Withdrawals at the beginning of next year (or end of the current year) = 1200 x (1/0.005) x [1-{1/(1.005)^(12)}] = $ 13942.72

Let the current required investment be $K

Therefore, K x (1.005)^(12) = PV1

K = 13942.72 / (1.005)^(12) = $ 13132.72

(B) Current Payout = $ 100, Cheque Amount = $ 120 and Tenure = 10 days

Holding Period Yield = HPY = [(120 - 100) / 100] x 100 = 20 %

Effective Annual Yield = [1+HPY]^(365/10) - 1 = 775.4535 or 77545.35 %

(C) Monthly Investments = $ 500, Interest Rate = 13.5 %, Deposit Tenure = 40 years or (40 x 12) = 480 months

Monthly Rate = (13.5 / 12) = 1.125 %

Therefore, Account Worth at Retirement = Total Future Value of All Monthly Deposits = 500 x (1.01125)^(479) + 500 x (1.01125)^(478) + ............+ 500 x (1.01125)^(1) + 500 = [{(1.01125)^(480) - 1} / {1.01125 - 1}] x 500 = $ 9503592.69