Marissa makes an initial deposit of $1,000. Her contributions are $100 a month for the next 40 years. She chooses to invest in the US stock market through an index fund with a 6.5% return annually.

Question

What is the balance of Marissa’s retirement account after 40 years?

Answer 1

This is an example of computing the future value of an annuity (or a constant periodic payment).

A 6.5% annual return equates to a simple monthly return of 6.5/12=0.54%= 0.0054 (in decimal terms).

Marissa has made an initial investment of $1000 and $100 every month for 40 years (480 months).

The future value of the monthly $100 payments is

100/r * [ (1+r)^n - 1 ] where r=0.0054 and n=480

To this add the future value of the initial $1000 which is 1000*(1 + 0.065)^40 and you get the total retirement balance after 40 years.