We can use the formula for compound interest:
\[A = P \left(1 + \frac{r}{n}\right)^{nt}\]
where $A$ is the final amount, $P$ is the principal (initial amount), $r$ is the annual interest rate (expressed as a decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the number of years.
In this problem, we have $P = 13,000$, $r = 0.03$, $n = 2$ (since interest is compounded semi-annually), and $t = 20$.
Plugging these values into the formula, we get:
\[A = 13000 \left(1 + \frac{0.03}{2}\right)^{(2)(20)}\]
Simplifying the exponent:
\[A = 13000 \left(1 + 0.015\right)^{40}\]
Carrying out the addition inside the parentheses:
\[A = 13000 \left(1.015\right)^{40}\]
Evaluating the expression inside the parentheses:
\[A = 13000 (1.7474220513)\]
Rounding to the nearest cent, we find $A \approx \boxed{22,716.47}$.
Suppose $13,000 is deposited into a savings account earning 3% interest compounded semi-annually. Find the balance in the account after 20 years. Round to the nearest cent.
Use one of these formulas to solve the problem.
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