Question

PPI wants to make five equal annual savings account deposits beginning June 1, Year 4, in order to be able to withdraw $75,000 at six annual intervals beginning June 1, Year 9. The amount on deposit with Idaho First Bank & Trust will earn 8% per annum until the account is exhausted. The controller asks you to compute the amount of the deposits that will be needed.

Answer 1

Withdrawal Value = $ 75000, Number of Withdrawals = 6 beginning June 1, year 9 and continuing up to June 1, year 14.

Let the amount of each deposite be $ P, Number of Deposits = 5 beginning June1, year 4 and continuing up to June 1, year 8.

Interest Rate = 8 % per annum

Present Value of Withdrawals on June 1, Year 8 = PV8 = 75000 x (1/0.08) x [1-{1/(1.08)^(6)}] = $ 346716

Future Value of Deposits on June 1, Year 8 = FV8 = P x (1.08)^(4) + P x (1.08)^(3) + P x (1.08)^(2) + P x (1.08) + P = P x [{(1.08)^(5)-1}/{1.08-1}]

Now, PV8 = FV8 so as to conform with the principles of time value of money.

Therefore. 346716 = P x [{(1.08)^(5) - 1}/{1.08-1}]

346716 = P x 5.866601

P = 346716 / 5.866601 = $ 59099.98