Question

The compound interest formula is A = P(1+) where P is the principal, A is the ending amount, r is the annual interest rate, mis

the number of compounding periods, and r is the number of years. Billy invests $5,000 in an account at 4.2 % for 15 years,
compounded monthly. Assuming no other deposits or withdrawals are made, how much will Billy have at the end of 15 years?
$9,377.73
$5,269.03
$6,750
$9,267.99

Answer 1

`~~~~~~ \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 &\$5000\\ r=rate\to 4.2\%\to (4.2)/(100)\dotfill &0.042\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}`

`A = 5000\left(1+(0.042)/(12)\right)^(12\cdot 15) \implies A = 5000( 1.0035)^(180)\implies A \approx 9377.73`