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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: [tex]V(t)=P(1+r/n)^n^t[/tex]
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

Sagot :

[tex]~~~~~~ \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 &\$500\\ r=rate\to 5\%\to \frac{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+\frac{0.05}{1}\right)^{1\cdot 3}\implies A=500(1.05)^3\implies A\approx 578.81[/tex]

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