Question

Use the compound interest formula to compute the balance in the following account after the stated period of time, assuming interest is compounded annually. $13,000 invested at an APR of 3.8% for 11 years. The balance in the account after 11 years is $______. (Round to the nearest cent as needed.)

Answer 1

The balance in the account after 11 years with a $13,000 initial investment at a 3.8% annual compound interest rate is $19,542.30.

Step-by-step explanation:

To compute the balance in an account after a certain period with compound interest, we use the formula:

A = P(1 + r/n)nowhere:P is the principal amount (the initial amount of money)r is the annual interest rate (in decimal form)n is the number of times that interest is compounded per yearn is the number of years the money is invested florin this case:P = $13,000r = 3.8% = 0.038n = 1 (since interest is compounded annually)t = 11 years Now we apply these values to the compound interest formula:A = $13,000(1 + 0.038/1)1*11A = $13,000(1.038)11A = $13,000(1.5032541)A = $19,542.30Therefore, the balance in the account after 11 years is $19,542.30.Conclusion: Compound interest is particularly powerful over the long term and can significantly increase the return on your initial investment. In this case, an initial investment of $13,000 grows to $19,542.30 after 11 years at an annual compound interest rate of 3.8%.