Question

Ronald is 26 years old and starting an IRA (individual retirement account). He is going to invest $200 at the beginning of each month. The account is expected to earn 2.75% interest, compounded monthly.How much money will Ricky have in his IRA when he retires, at age 65? $434,065.20 $167,868.30 $86,350.79 $14,053.63

Answer 1

The formula for the future value A, given annual interest rate r, number of years t, and deposit amount P can be written as

... A = P(1 +r/12)((1+r/12)^(12t) -1)/(r/12)

Filling in the given numbers, you have

... A = 200(1+.0275/12)((1+.0275/12)^(12·39) -1)/(.0275/12) ≈ 167,868.30

The appropriate choice is $167,868.30.

_____

The formula is the one for the sum of a geometric series. It can be useful to consider the last deposit made as the first term of the series.