Question

If an investor age 25 deposits $100 a month in a mutual fund with an annualized return of 10% a year, he'll have about $640,000 at age 65. If he waits until age 40 to start saving, how much will he have to deposit each month to have the same amount at age 65?

A. $150

B. $225

C. $475

D. $800

Answer 1

Given

Future value of annuity=$640000.

Intrest(i)=10%per year

Period=65years-40uears

=25years

Here we pay monthly so we want to calculate interest per month.

Intrest rate per month =10/12=0.833

Future value annuity=A*((1+i)ⁿ-1)/i

Here. A=Annuity payment

i=intrest rate.

n= period

$640000=A*((1+0.00833)^25*12-1)/0.00833

$640000=A*((1.00833)³⁰⁰-1)/0.00833

$640000=A*(12.044-1)/0.00833

$640000=A*11.044/0.00833

A=$640000*0.00833/11.044

A=$482

Annuity =$482

Monthly payment required =$482

Approximately $375.

Note:in the question given that he get $640000 at his 60th year so we treat that amount as future value.