Final answer:
To find the future value of a $20,000 investment compounded quarterly at a 2.75% annual interest rate for 12 years, apply the compound interest formula. The future value is calculated to be $27,785.89, meaning the interest earned on this investment is $7,785.89.
Step-by-step explanation:
The future value of a fixed investment can be found using the compound interest formula. In this case, we want to find the future value of a $20,000 investment at a 2.75% annual interest rate, compounded quarterly, over a period of 12 years. The formula to calculate future value is:
Future Value = Principal × (1 + (Interest Rate / Number of Compounds))^(Number of Compounds × Time)
First, we must adjust the annual interest rate to the quarterly rate by dividing it by 4 (since there are four quarters in a year), so the quarterly interest rate is 2.75% / 4 = 0.6875%. Next, we'll convert this percentage into a decimal for our calculations, which would be 0.006875. Then we can apply it to the formula:
Future Value = $20,000 × (1 + 0.006875)^(4 × 12)
Calculating the exponent part first:
(1 + 0.006875)^(4 × 12) = (1 + 0.006875)^48 ≈ 1.3892944
Next, multiply this by the principal:
Future Value ≈ $20,000 × 1.3892944 = $27,785.89
The interest earned is the future value minus the original principal:
Interest Earned = Future Value - Principal
Interest Earned = $27,785.89 - $20,000 = $7,785.89
Therefore, the investment will grow to $27,785.89 after 12 years, and the interest earned will be $7,785.89.