Question

On your 22^nd birthday, you decided to invest $5,000 in a mutual fund that earns 7% per year. You continue to make this deposit every year until you retire at the age of 67. You expect your salary to increase by an average of 4% each year during the time and this will increase your annual deposit by 4%. How much money will you have accumulated in your mutual fund when you retire?

Answer 1

This is a case of growing annuity, where the starting payment (P) is $5000, growth rate (g) is 4%, rate of return (r) is 7%, number of periods (n) is 45, i.e., 67-22 years

The formula for future value of annuity, i.e., what will be available at teh end of 45 years is:

FV = P*((1+r)^n - (1+g)^n)/(r-g)

= $5000*((1.07^45)-(1.04^45))/(0.07-0.04)

= $2,526,879