Question

You just turned 30 years old, and decided that it is time to start saving for retirement. Based on

your anticipated income and expenses, you expect to be able to invest $4,000 each year until you

are 50 years old, and then $5,000 each year until you retire at age 65.

You expect to earn 6.1% on your investments. What is the expected value of your retirement

account at age 65?

During retirement, you expect to spend about $160000 per year. You expect to live until you are

85 years old, and will continue to earn 6.1% on your remaining investments until you die. How

much do you need to have saved at age 65 to fund your retirement? Is your retirement completely

funded by your investments?

You just received a large inheritance. If your retirement is not completely funded by your

investments, how much of the inheritance do you need to set aside now (at age 30) to fund the

remainder of your retirement needs, if you expect to earn 6.1% on your investments?

Hint: for the time period 30-50, take N=20 and for the time period 50-65 take N=15

Answer 1

$4000 is invested for 50-30 =20 years and $5000 for 65-50=15 years

r=6.1%

Hence FV at age 50 of $4000 = 4000*((1+6.1%)^20-1)/6.1%

=4000*((1.061)^20-1)/0.061

=4000*(3.2682-1)/0.061

=4000*2.2682/0.061

=148733.96

FV at age 65 = 148733.96*(1+15%)^15 = 148733.96*1.061^15 = 148733.96*2.4307=$361527.13

Hence FV at age 65 of $5000 = 5000*((1+6.1%)^15-1)/6.1%

=5000*((1.061)^15-1)/0.061

=5000*(2.4307-1)/0.061

=5000*1.4307/0.061

=$117270.22

Total FV = 361527.13+117270.22=$478797.35

$160000 will be spent for 85-65=20 years, hence PV = 160000*(1-(1+6.1%)^-20)/6.1%

=160000*(1-(1.061)^-20)/0.061

=160000*(1-0.3118)/0.061

=160000*(0..6882)/0.061

Amount required at age 65=$1805102.36

Hence the amount saved is not sufficient to fund retirement needs

Extra amount required = 1805102.36-478797.35=1326305.01

Hence the amount of inheritance at age 30 will grow for 35 years at 6.1%

Hence PV = 1326305.01/(1+6.1%)^35 = 1326305.01/1.061^35=1326305.01/7.6861=$172559.20

Hence $172559.20 needs to be set aside from inheritance for remaining needs