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+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$11250\\ r=rate\to 3\%\to (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(1)/(2)\dotfill &4.5 \end{cases}`

`\bf A=11250\left(1+(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.