Respuesta :
Answer:
The answer is : $67,266.16
Step-by-step explanation:
This question is a future value question.
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 =[tex]3200+1600=4800[/tex] 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
The amount saved in 10 years is [tex]\boxed{\$ 67266.20}.[/tex]
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,
[tex]\boxed{{\text{Future Value}} = {\text{P}} \times \frac{{{{\left( {1 + \frac{i}{n}} \right)}^{nt}}}}{{\frac{i}{n}}}}[/tex]
Given:
Total salary is [tex]\$ 32000.[/tex]
The interest rate is [tex]7.3\%.[/tex]
Trent save [tex]10\%[/tex] of his salary every year.
Company puts [tex]5\%[/tex] of salary every year.
Calculation:
The [tex]10\%[/tex] of [tex]\$32000[/tex] can be calculated as follows,
[tex]\begin{aligned}{\text{Amount}}&= \frac{{10}}{{100}} \times 32000\\&= \$ 3200\\\end{aligned}[/tex]
The amount that company put can be obtained as follows,
[tex]\begin{aligned}{\text{Company Amount}} &= \frac{5}{{100}} \times 32000\\&= \$ 1600\\\end{aligned}[/tex]
The total amount can be calculated as follows,
[tex]\begin{aligned}{\text{Amount}} &= 3200 + 1600\\&= \$ 4800\\\end{aligned}[/tex]
The future value can be obtained as follows,
[tex]\begin{aligned}{\text{FV}} &= 4800 \times \frac{{{{\left( {1 + 0.073} \right)}^{10}} - 1}}{{0.073}} \\ &= 4800 \times 14.014\\&= \$ 67266.20\\\end{aligned}[/tex]
Hence, the amount saved in 10 years is [tex]\boxed{\$ 67266.20}.[/tex]
Learn more:
- Learn more about inverse of the function https://brainly.com/question/1632445
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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.
