Question

Derek decides that he needs $195,026.00 per year in retirement to cover his living expenses. Therefore, he wants to withdraw $195026.0 on each birthday from his 66th to his 87.00th. How much will he need in his retirement account on his 65th birthday? Assume a interest rate of 8.00%.

Answer format: Currency: Round to: 2 decimal places.

Answer 1

Cash flow = $ 195026

Periods = 22 ( 66 to 87 years)

Payout Annuity : you made an investment intially and it gives cash flows over the periods

Particulars	Amount
Cash Flow	$        195,026.00
Int Rate	8.0000%
Periods	22

Present Value of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 195026 * [ 1 - [(1+0.08)^-22]] /0.08
= $ 195026 * [ 1 - [(1.08)^-22]] /0.08
= $ 195026 * [ 1 - [0.1839]] /0.08
= $ 195026 * [0.8161]] /0.08
$1,989,410.23

r - Int rate per period
n - No. of periods
If Derek have $ 1989410.23 in his account on his 65^th Birthday , every year he can receive $ 195026 over the period of his 66^th Birthday to 87^th Birthday .

Please comment if any assistance is required