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Question

# Use the compound interest formula to compute the balance in the following accounts after the stated period of time, assuming interest is compounded annually.$\ 3000$ is invested at an $\mathrm{APR}$ of $1.8 \%$ for $12$ years.

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To get the accumulated value of an investment of $\textcolor{#c34632}{\3,000}$ at an annual percentage rate of $\textcolor{#c34632}{1.8\%}$ for $\textcolor{#c34632}{12 \ \text{years}}$, we will use this formula:

\begin{aligned} A= P \times(1 + APR)^Y \end{aligned}

where $A$ is the accumulated balance after $Y$ years, $P$ is the starting principal, $APR$ is the annual percentage rate in decimal form, and $Y$ is the time in years.

Plugging in the known values, we have

\begin{aligned} A &= \3,000 \times (1 + 0.018)^{12} \\ &\approx \boxed{\3,716.16} \end{aligned}

The accumulated value after $10$ years is approximately $\textcolor{#4257b2}{\3,716.16}$.

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