Question

jamie is 22 years old and works for a company that matches her 401(k) contribution up to 3%. the interest rate for her 401(k) is 8%. if she puts away 9.5% of her $41,000 salary every year, how much would she have saved in 10 years? round your answer to the nearest cent.
a. $34,389.17
b. $37,140.30
c. $80,183.12
d. $74,243.63
please select the best answer from the choices provided

Explanation:

Step1: Calculate annual employee contribution

First, find 9.5% of Jamie's $41,000 salary.
$\text{Employee Contribution} = 0.095 \times 41000 = 3895$

Step2: Calculate annual employer match

The company matches up to 3% of her salary.
$\text{Employer Match} = 0.03 \times 41000 = 1230$

Step3: Total annual contribution

Sum employee and employer annual contributions.
$\text{Total Annual Contribution} = 3895 + 1230 = 5125$

Step4: Use annuity future value formula

The future value of an ordinary annuity formula is $FV = P \times \frac{(1+r)^n - 1}{r}$, where $P=5125$, $r=0.08$, $n=10$.
First calculate $(1+0.08)^{10}$:
$(1.08)^{10} \approx 2.158925$
Then compute the numerator:
$2.158925 - 1 = 1.158925$
Divide by the interest rate:
$\frac{1.158925}{0.08} \approx 14.48656$
Multiply by total annual contribution:
$FV = 5125 \times 14.48656 \approx 74243.63$

Answer:

d. $74,243.63