Question

Your older brother turned 35 today, and he is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. He will invest in a mutual fund that's expected to provide a return of 7.5% per year. He plans to retire 30 years from today, when he turns 65, and he expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can he spend each year after he retires?

Answer 1

Answer:

Elder Brother will be able to annual spend $64,932.21 each year for 25 years after retirement.

Explanation:

The question is to find the Future Value of saving $7,000 per year for retirement.

First step is to know the formula for the Future of Annuity in order to compute the future value of his yearly deposits.

Future Value (FV) = $P * (1+r)^{n}- 1/r]$

FV= Future value of the annuity

P= The annual payments/savings

r = rate for each period

n= number of years he is to save

FV = $7,000 * (1+0.075)^{30}- 1/0.075]

= $7,000 x (8.754955-1/0.075

=$7,000 x (7.754955/0.075)

= $723,795.82

The answer above shows the amount of cash flow, his current yearly savings will make available for him at the age of 65 and to be spent for the 25 years he expects to live after retirement.

Using the amount therefore, we can determine the amount he is able to spend each year as follows

PV (at the time of his retirement)= P x [1-(1+r)^{-n}/r]

Where PV= $723,795.82

P= Expected periodic spending per year after retirement

R = Rate for each period = 7.5%

n= number of years expected after retirement= 25 years

$723,795.82= P x [1-(1+0.075)^{-25}/0.075]

$723,795.82= P [(1-0.163979)/0.075]

$723,795.82= P x (0,836021 /0.075)

$723,795.82= P x 11.14695

P= $723,795.82=/11.14695

P= $64,931.21

This means Elder Brother will be able to annual spend $64,932.21 each year for 25 years after retirement.