Question

How much is compound interest earned on $11,250 principal, with an annual interest rate of 3% compounded annually, over 4 1/2 years?
compound interest: A = P (1 + r)t


A.$1518.75


B.$1600.50


C.$12,869.55


D.$12,850.50

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 11250\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\to 4\frac{1}{2}\dotfill &4.5 \end{cases}$

$\bf A=11250\left(1+\frac{0.03}{1}\right)^{1\cdot 4.5}\implies A=11250(1.03)^{4.5}\implies A\approx 12850.50 \\\\\\ \stackrel{\textit{earned interest}}{12850.50-11250}\implies 1600.50$

so in  short, the accumulated amount minus the original amount = interest.