Trent is 25 years old and works for a company that matches his 401(k) contribution up to 5%. The interest rate for his 401(k) is 7.3%. If he puts away 10% of his $32,000 salary every year, how much would he have saved in 10 years? Round your answer to the nearest cent.

As given, Trent puts away 10% of his $32,000 every year and the company will put half amount of $1,600. So, total amount becomes =@@MATH_TOKEN_0@@ each year.

Formula for future value or FV is Fv = Pmt (1 + r/n)^(nt) – 1 / (r/n)

Where, Fv = Future Value , Pmt = repeated payments , R = interest rate ,N = total number of payment periods

Putting the values in the formula,

Fv = 4800 (1 + 0.073/1)^(1x10) – 1 (0.073/1)

Fv = $67266.16

Hence, the answer is $67266.16

AkshayG AkshayG · Answer 2 · 2019-11-30T01:23:43-05:00

The amount saved in 10 years is $\boxed{\$ 67266.20}.$

Further Explanation:

Annuity is a series of payment that is made after equal interval of time.

Future value of annuity of payment P for n year if the return is i can be expressed as,

$\boxed{{\text{Future Value}} = {\text{P}} \times \frac{{{{\left( {1 + \frac{i}{n}} \right)}^{nt}}}}{{\frac{i}{n}}}}$

Given:

Total salary is $\$ 32000.$

The interest rate is $7.3\%.$

Trent save $10\%$ of his salary every year.

Company puts $5\%$ of salary every year.

Calculation:

The $10\%$ of $\$32000$ can be calculated as follows,

$\begin{aligned}{\text{Amount}}&= \frac{{10}}{{100}} \times 32000\\&= \$ 3200\\\end{aligned}$

The amount that company put can be obtained as follows,

$\begin{aligned}{\text{Company Amount}} &= \frac{5}{{100}} \times 32000\\&= \$ 1600\\\end{aligned}$

The total amount can be calculated as follows,

$\begin{aligned}{\text{Amount}} &= 3200 + 1600\\&= \$ 4800\\\end{aligned}$

The future value can be obtained as follows,

$\begin{aligned}{\text{FV}} &= 4800 \times \frac{{{{\left( {1 + 0.073} \right)}^{10}} - 1}}{{0.073}} \\ &= 4800 \times 14.014\\&= \$ 67266.20\\\end{aligned}$

Hence, the amount saved in 10 years is $\boxed{\$ 67266.20}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Investment and return

Keywords: Trent, 25 years old, works, company, matches, 401(k), 7.3%, 10%. $32000, salary, every year, 10 years, amount, 5%, nearest cent.