Question

Assume that you plan to retire in 30 years and hope to have $1.5 million in savings when you retire. If you can earn 6% annually on your investments, how much do you need to save each year? If you are instead able to earn 8% annually, how much do you need to save each year? In either case, if you divide the annual amount by 12 and save that amount each month, will your final result be more or less than $1.5 million (assuming that your interest rate assumption is correct).

Answer 1

We are given the future value of an annuity in this question. The future value is computed as follows -

where, A = periodic payments, r = rate of interest, n = no. of periods

If rate is 6%

FV = $1,500,000, r = 6%, n = 30

or, A = $18,973.37

If this amount is dividend by 12, monthly payment would be $1,581.11. Now, we need the future value of this amount -

A = $1,581.11 , r = 6% / 12 = 0.5%, n = 30 x 12 = 360

which is more than $1.5 million.

If rate is 8%

FV = $1,500,000 , r = 8%, n = 30

or, A = $13,241.15

If we divide this number by 12, monthly payment would be $1,103.43. Future value of this amount would be -

A = $1,103.43, n = 360, r = 8% / 12 = 0.6666666666%

which is also more than $1.5 million.