Respuesta :
Answer:
A. $52,835.72
Step-by-step explanation:
We have been given that Will is 30 years old and works for a company that matches his 401(k) contribution up to 3%. The interest rate for his 401(k) is 7.13%. He puts away 9% of his $41,000 salary every year.
First of all, we will find amount deposited by Will each year in his 401(k) by calculating 9% of $41,000 as:
[tex]\text{Amount deposited by Will in his 401(k)}=\$41,000\times \frac{9}{100}[/tex]
[tex]\text{Amount deposited by Will in his 401(k)}=\$41,000\times 0.09[/tex]
[tex]\text{Amount deposited by Will in his 401(k)}=\$3690[/tex]
Now, we need to calculate 3% of $3690 to find amount deposited by the company in Will's 401(k).
[tex]\text{Amount deposited by company in Will's 401(k)}=\$3690\times \frac{3}{100}[/tex]
[tex]\text{Amount deposited by company in Will's 401(k)}=\$3690\times 0.03[/tex]
[tex]\text{Amount deposited by company in Will's 401(k)}=\$110.7[/tex]
[tex]\text{Total amount deposited in Will's 401(k)}=\$3690+\$110.7[/tex]
[tex]\text{Total amount deposited in Will's 401(k)}=\$3800.7[/tex]
Now, we will use regular deposits formula to find amount in Will's 401(k) after 10 years.
[tex]A=M((1+\frac{i}{q})^{nq}-1)(\frac{q}{i})[/tex], where,
A = Final amount n years,
M =Amount deposited per period,
i = Interest rate in decimal form,
q = Number of deposits in one year,
n = Number of years.
Upon substituting our given values in above formula, we will get:
[tex]A=\$3800.7((1+\frac{0.0713}{1})^{10*1}-1)(\frac{1}{0.0713})[/tex]
[tex]A=\$3800.7((1+0.0713)^{10}-1)(14.0252454417952)[/tex]
[tex]A=\$3800.7((1.0713)^{10}-1)(14.0252454417952)[/tex]
[tex]A=\$3800.7(1.9911824193596552-1)(14.0252454417952)[/tex]
[tex]A=\$3800.7(0.9911824193596552)(14.0252454417952)[/tex]
[tex]A=\$52,835.722598320239[/tex]
Round to nearest cent:
[tex]A\approx \$52,835.72[/tex]
Therefore, Will would have saved $52,835.72 in 10 years and option A is the correct choice.
