Question

A customer deposits $500 in an account that pays 5% annual interest.

What is the balance after 3 years if the interest is compounded annually? Round your answer to the nearest cent.
Compound interest formula:
`V(t)=P(1+r/n)^n^t`
t = years since initial deposit
n = number of times compounded per year
r = annual interest rate (as a decimal)
P = initial (principal) investment
V(t) = value of investment after t years

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 &\$500\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=500\left(1+(0.05)/(1)\right)^(1\cdot 3)\implies A=500(1.05)^3\implies A\approx 578.81`