If $25,000 is invested for 15 years compounded quarterly and grows to $52,680. Find the interest rate to the nearest percent.

Jaya Legge 2021-06-07 Answered
If $25,000 is invested for 15 years compounded quarterly and grows to $52,680. Find the interest rate to the nearest percent.

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Expert Answer

Clelioo
Answered 2021-06-08 Author has 17199 answers

Use the compound interest formula: \(\displaystyle{A}={P}{\left({1}+\frac{{r}}{{n}}\right)}^{{n}}{t}\)
where A is the final value, P is the present value, r is the rate (in decimal form), and n is compounding times per year, and t is the time in years.
Substitute A=52680, P=25000, n=4 for quarterly, and t=15 then solve for r: \(\displaystyle{52680}={25000}{\left({1}+\frac{{r}}{{4}}\right)}^{{4}}{\left({15}\right)}\)
\(\displaystyle{52680}={25000}{\left({1}+\frac{{r}}{{4}}\right)}^{{60}}\)
Divide both sides by 25000: \(\displaystyle{2.1072}={\left({1}+\frac{{r}}{{4}}\right)}^{{60}}\)
Raise both sides by \(\displaystyle\frac{{1}}{{60}}\): \(\displaystyle{2.1072}={1}+\frac{{r}}{{4}}\)
Subtract 1 from both sides: \(\displaystyle{\left(\frac{{2.1072}^{{1}}}{{60}}\right)}-{1}=\frac{{r}}{{4}}\)
Multiply both sides by 4: \(4((2.1072^1/60)-1)=r r=0.05->5%\)

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Answered 2021-10-10 Author has 11827 answers

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