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.

1 answer

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 $A \approx \boxed{22,716.47}$.