Final answer:
The future value of $8700 invested for 13 years at a 10% interest rate compounded semiannually is approximately $37,339.68, calculated using the compound interest formula.
Step-by-step explanation:
The future value of an investment is calculated using the compound interest formula, which is A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, t is the time in years. For an investment of $8700 at a 10% interest rate compounded semiannually for 13 years, the calculation would involve plugging these values into the formula:
A = $8700(1 + 0.10/2)^(2 × 13)Calculating this, we get:A = $8700(1 + 0.05)^(26)A = $8700(1.05)^26A = $8700 × 4.29187072A ≈ $37,339.68Thus, the future value of $8700 invested for 13 years at 10% compounded semiannually is approximately $37,339.68.The future value of an investment can be calculated using the formula:Future Value = P(1+r/n)^(nt)Where:P is the principal amount ($8700)r is the annual interest rate (10% or 0.1)n is the number of times interest is compounded per year (2 for semiannualt is the number of years (13Substituting the values into the formula, we get:Future Value = $8700(1 + 0.1/2)^(2*13)Calculating this using a calculator or spreadsheet, the future value of the investment is approximately $28,792.55.