Answer to Question #254756 in Financial Math for Katie

Question

Jeni has decided that she needs to start saving for her retirement. She can afford $100 a month deducted automatically from her paycheck. She deposits it into an account that earns 4.5% interest compounded monthly. How much will she have in her account when she retires 42 years later? A. $ 14,922.70 B.$ 50,400.00 C. $132,213.00 D. $149,226.96

Answer 1

The account value at retirement can be calculated with the help of future value of annuity function.

$FV \space of\space annuity = Monthly\space deposit×((1+Rate)^N−1)\div Rate\\ where \space rate = 4.50\%\div 12 = 0.375\%$

$and\space N = 42 years×12 months = 504 months\\$

$FV \space of\space annuity = \$100×((1+0.375\%)^{504}−1)\div 0.375\%$

$= \$100×1492.269621\\=\$149,226.96$

Future value at retirement = $149,226.96

Correct choice D