Question

Ashley and Dwayne are saving for retirement. Their goal is to have $250,000 in 15 years. They open up an account with APR of 3.7% compounded monthly. How much should they deposit each month to meet their goal?

Answer 1

The formula for the future value of an investment with regular contributions is

FV = M((1+r/n)^(nt)-1)(n/r)

where

FV = Future value

M = Deposit per period

r = Interest rate

n = number of periods per year

t = number of years

So let's solve for M, then substitute the known values and calculate:

FV = M((1+r/n)^(nt)-1)(n/r) FV/(((1+r/n)^(nt)-1)(n/r)) = M

250000/(((1+0.037/12)^(12 * 15)-1)(12/0.036)) = M

250000/(((1+0.003083333)^(180)-1)(324.3243243)) = M

250000/(((1.003083333)^(180)-1)(324.3243243)) = M

250000/((1.740454228-1)(324.3243243)) = M

250000/240.1473172 = M

1041.027661 = M

So the monthly deposit should be 1041.03 every month.

Note: This calculation assumes that the 1st deposit will happen AFTER the 1st month.