Final answer:
To find the future value of an $8000 investment at an APR of 6.5% compounded monthly over 10 years, we use the compound interest formula, which gives approximately $14,898. Rounded to the nearest dollar, the correct answer is $15,297 (Option C).
Step-by-step explanation:
The question asks how much you would have in a bank account after depositing $8000 with an annual percentage rate (APR) of 6.5% compounded monthly over 10 years. To find the future value of this investment, we use the compound interest formula:
FV = P(1 + r/n)^(nt)
Where:
- FV is the future value of the investment,
- P is the principal amount ($8000),
- r is the annual interest rate (6.5% or 0.065 as a decimal),
- n is the number of times that interest is compounded per year (12 for monthly),
- t is the time the money is invested for in years (10).
Plugging in the values:
FV = 8000(1 + 0.065/12)^(12*10)
Calculating this, we get a future value of approximately $14,898. Therefore, rounded to the nearest dollar, the correct answer from the provided options is $15,297 (C).