Josalynn

## Answered question

2021-01-10

Solve the compound interest formula for the interest rate r using the properties of rational exponents. then use the obtained formula to calculate the interest rate for an account that was compounded semi-annually, had an initial deposit of \$10,000 and was worth \$14,373.53 after 11 years.

### Answer & Explanation

faldduE

Skilled2021-01-11Added 109 answers

$\because 14,373.53=10,000\left(1+\frac{r}{2}{\right)}^{2}\left(11\right)$
$⇒14,373.53=10,000\left(1+\frac{r}{2}{\right)}^{22}$
$⇒\frac{14,373.53}{10000}=\left(1+\frac{r}{2}{\right)}^{22}$
$⇒\left(1+\frac{r}{2}{\right)}^{22}=\frac{14,373.53}{10000}$
$⇒\left(1+\frac{r}{2}{\right)}^{22}=1.437353$
$⇒In\left(\frac{1+r}{2}{\right)}^{22}=In\left(1.437353\right)$
$⇒22In\left(\frac{2+r}{2}\right)=In\left(1.437353\right)$
$⇒In\left(2+r\right)=\frac{In\left(1.437353\right)}{22}+In2$
$⇒\left(2+r\right)=e\frac{In\left(1.437353\right)}{22}+In2\right)$
$⇒r=e\frac{In\left(1.437353\right)}{22}+In2\right)$
$⇒r=0.03325$
$⇒r=3.325\mathrm{%}$

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