Final answer:
Using the formula I = PRT, where P is the principal, R is the annual interest rate, and T is time in years, the total interest earned on the investment after 15 years at 5.7% is $32,062.50. The future value of the investment, which is the sum of principal and interest, is $57,062.50.
Step-by-step explanation:
To determine the future value of the interest of a simple interest investment with a 15-year term at 5.7% on a deposit of $25,000, we can use the formula for calculating simple interest:
I = PRT
where:
- I is the interest,
- P is the principal amount ($25,000),
- R is the annual interest rate (5.7%, or 0.057 as a decimal),
- T is the time in years (15 years).
Plugging the values into the formula, we get:
I = $25,000 × 0.057 × 15
I = $2,137.50 × 15
I = $32,062.50
Therefore, the total interest earned over the 15 years is $32,062.50. The future value of the investment is then the principal plus the interest, which equals:
Future Value = P + I
Future Value = $25,000 + $32,062.50
Future Value = $57,062.50
The options provided do not include this value. However, if we are asked to find only the future interest (not the total future value), we can settle on the interest amount of $32,062.50.