[tex] \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 &\$20000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} [/tex]
[tex] \bf A=20000\left(1+\frac{0.055}{1}\right)^{1\cdot 10}\implies A=20000(1.055)^{10} \\\\\\ A\approx 34162.88916707\implies A\approx \stackrel{\textit{rounded up}}{34162.89} [/tex]
The value of the amount after 10 years is $34,000.
Jill invested $20,000 in an account that earned 5.5% annual interest, compounded annually.
What is the value of this account after 10 years?
The amount after 10 years is determined by following formula;
[tex]\rm Amount = Principal \times \left (1 + \dfrac{Rate }{100} \right )^{Time}[/tex]
Where Principal = $20,000, rate = 5.5%, and time = 10 years
Substitute all the values in the formula;
[tex]\rm Amount = Principal \times \left (1 + \dfrac{Rate }{100} \right )^{Time}\\\\\rm Amount = 20000 \times \left (1+\dfrac{5.5}{100}\right )^{10}\\\\Amount = 20000 \times (1+0.55)^{10}\\\\Amount = 20000 \times(1.055)^{10}\\\\Amount = 20000 \times 1.70\\\\Amount = 34,000[/tex]
Hence, the value of the amount after 10 years is $34,000.
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