Submit quiz
Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity if $\$ 10$ is invested semiannually for 15 years at $6.0 \%$ compounded semiannually.
\[
A=\frac{p\left[\left(1+\frac{r}{n}\right)^{n t}-1\right]}{\frac{r}{n}}
\]

The accumulated amount wil be $\$$
(Round to the nearest cent as needed)
Time Remaining: 00:59:36

Step 1 ：The question is asking for the accumulated amount in an annuity given certain parameters. The formula provided is for an ordinary annuity, which is a sequence of equal payments made at the end of each period over a fixed amount of time. The parameters given are: p (the payment per period): $10, r (the annual interest rate): 6.0%, n (the number of compounding periods per year): 2 (since it's semiannually), t (the number of years): 15.

Step 2 ：We can substitute these values into the formula to find the accumulated amount. The formula is \(A=\frac{p\left[\left(1+\frac{r}{n}\right)^{n t}-1\right]}{\frac{r}{n}}\).

Step 3 ：Substituting the given values into the formula, we get \(A=\frac{10\left[\left(1+\frac{0.06}{2}\right)^{2 \times 15}-1\right]}{\frac{0.06}{2}}\).

Step 4 ：Solving the equation, we find that the accumulated amount is approximately $475.75.

Step 5 ：Final Answer: The accumulated amount will be approximately \(\boxed{\$475.75}\).