Final answer:
The future value of a $2,577 investment at 2% compounded semiannually for two years is approximately $2,681.24. Therefore, the closest answer choice is c) $2,688.62, given the options provided.
Step-by-step explanation:
To determine the future value of a $2,577 investment at 2% interest compounded semiannually for two years, we can use the compound interest formula:
Future Value = P (1 + r/n)^(nt)
Where:
- P = Principal amount ($2,577)
- r = Annual interest rate (2%)
- n = Number of times the interest is compounded per year (2 for semiannual)
- t = Number of years the money is invested (2)
Calculating this we get:
Future Value = $2,577 * (1 + 0.02/2)^(2*2)
Future Value = $2,577 * (1 + 0.01)^(4)
Future Value = $2,577 * (1.01)^4
Future Value = $2,577 * 1.04060401
Future Value = $2,681.24
So the closest option to our calculated future value is c) $2,688.62, assuming the investment is compounded exactly semiannually and there are no additional fees or considerations that might affect the final amount.