Questions: Use the appropriate compound interest formula to compute the balance in the account after the stated period of time 13,000 is invested for 5 years with an APR of 5% and quarterly compounding. The balance in the account after 5 years is (Round to the nearest cent as needed.)

Solution Steps

To convert the APR from a percentage to a decimal, divide by 100: \(r = \frac{5}{100} = 0.05\).

The rate per period is calculated by dividing the annual rate by the number of compounding periods per year: \(\frac{r}{n} = \frac{0.05}{4} = 0.0125\).

The total number of compounding periods is the product of the number of years and the number of compounding periods per year: \(n \times t = 4 \times 5 = 20\).

The final account balance is calculated using the formula: \(A = P \left(1 + \frac{r}{100n}\right)^{nt} = 13000 \times \left(1 + 0.0125\right)^{20} = 16666.484\).

The final account balance, rounded to 2 decimal places, is: $16666.48.

Final Answer: