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When you start your career, you decide to set aside $500 every quarter to deposit into an investment account. The investment firm claims that historically their accounts have earned an annual interest rate of 10.0% compounded quarterly. Assuming this to be true, how much money will your account be worth after 25 years of depositing and investing? Round your answer to the nearest cent. Do not include labels or units. Just enter the numerical value.



Answer :

Given:

The principal amount = $500

Interest rate = 10% quarterly

Required:

Find the deposing amount after 25 years.

Explanation:

The amount formula when the interest is compounded quarterly is given as:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where r = interest rate

t = time period

n = The number of compounded times

The amount after 25 years is:

[tex]\begin{gathered} A=500(1+\frac{0.1}{4})^{4\times25} \\ A=500(1+.025)^{100} \\ A=500(1.025)^{100} \end{gathered}[/tex][tex]\begin{gathered} A=500\times11.81371 \\ A=5906.8581 \end{gathered}[/tex]

Final Answer:

The amount after 25 years will be &5906.85

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