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 \(\boxed{\$475.75}\).