Question

You calculate you’ll need $2,600,000 saved for retirement when you plan to retire in 40 years. You think you will earn 12% per year on your investments (ignore taxes) and currently have no savings. You want to save the same amount each month going forward (i.e. your monthly contribution to your retirement fund will always be the same), and you will save this amount at the end of each month. How much money do you need to save each month in order to reach your goal?

Answer 1

This is an annuity question. The payment per month (P) needs to be calculated for a given Future Value (FV) of $2,600,000.

FV of an annuity = P[(1+r)^n -1]/r

so, P = FV*r/[(1+r)^n -1]

annual interest rate R = 12%

so, monthly interest rate r is calculated as:

(1+r)^12 = (1+R)

r = (1+R)^(1/12) -1 = (1+12%)^(1/12) - 1= 0.95%

number of payments to be made (n) = 40*12 = 480

Thus, P = FV*r/[(1+r)^n -1]

= 2,600,000*0.95%/[(1+0.95%)^480 -1]

= 24,670.86/92.051

= 268.01

Thus, the monthly contribution to the retirement fund = $268.01 (Answer)