Question

When he retires, John Smith would like to be able to withdraw $ 40,000 annually at the beginning of each year for 40 years. How much should John Smith need to have in his account when he retires, so that he will be able to do this (interest rate is 5%)?

		$ 686,363.4
		$ 720,681.6
		$ 1,098,767.2
		$ 987,654

Answer 1

Formula for PV of annuity due is:

PV = P + P x [1-(1+r) -(n-1)/r]

P = Periodic cash withdrawal = $ 40,000

r = Periodic interest rate = 0.05

n = Number of periods = 40

PV = $ 40,000 + $ 40,000 x [1 – (1+ 0.05) -(40-1)/0.05]

    = $ 40,000 + $ 40,000 x [1 – (1.05) -39/0.05]

    = $ 40,000 + $ 40,000 x [(1 – 0.149147966415292)/0.05]

    = $ 40,000 + $ 40,000 x (0.850852033584708/0.05)

    = $ 40,000 + $ 40,000 x 17.0170406716942

   = $ 40,000 + $ 680,681.626867767

    = $ 720,681.626867767 or $ 720,681.6

Mr. John Smith should have $ 720,681.6 in his account on retirement to achieve the financial goal.

Hence option “$ 720,681.6” is correct answer.