Question

Heidi contributes 11% of her monthly salary towards her 401(k) and her employer matches her contribution up to 6% of her salary. If the interest rate of her 401(k) is 6.25% compounded monthly and her monthly salary is $3,250, determine the amount in her account after 15 years. Round to the nearest cent.

a.
$164,146.52
b.
$165,001.45
c.
$112,585.20
d.
$113,171.58

Answer 1

Heidi and her employer together contribute 11% + 6% = 17% of her monthly salary:
Monthly contribution P = 0.17(3,250) = $552.50.

Monthly interest rate i = 0.0625/12 = 0.005208333333...
Number of months n = 15 · 12 = 180.

Future value of an ordinary monthly annuity:
FV = P · [((1 + i)^n − 1) / i]
= 552.50 · [((1 + 0.0052083333)^180 − 1) / 0.0052083333]
≈ $164,146.52.

Answer: a. $164,146.52