Question

You are planning to make monthly deposits of $150 into a retirement account that pays 13 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 22 years?

Multiple Choice

• $2,690,863.46

• $235,450.55

• $213,026.69

• $189,883.81

• $224,238.62

Answer 1

Present Value, (PV) = 0

Monthly Deposit, (PMT) = $150

Time Period, (N) = 264 months

Interest Rate, (I) = 13%

Calculating Future Value,

Using TVM Calculation,

FV = [PV = 0, PMT = 150, N = 264, I = 0.13/12]

FV = $224,238.62

So,

Future Value in 22 years = $224,238.62

Answer 2

SOLUTION :

Monthly compounding.

Monthly deposit, A = 150 ($)

Monthly interest rate, r = 13/12 % = 13/1200 in fractions.

=> 1 + r = 1213/1200 

Periods, n = 22 * 12 = 264 months

So, 

FV after 22 years (264 months)

= A((1 + r)^n - 1) / r

= 150 * ((1213/1200)^264 - 1) / (13/1200)

= 224238.62 ($)  : 5th OPTION (ANSWER).