Final answer:
The future value of $1,708 with an 8.2% interest rate compounded semiannually for 15 years is calculated using the compound interest formula. The variables needed are the present value, interest rate, compounding frequency, and time period. By applying these values to the formula, one can determine the amount the initial investment will grow to over the specified duration.
Step-by-step explanation:
The future value of $1,708 after 15 years, assuming an interest rate of 8.2 percent compounded semiannually, can be calculated using the compound interest formula:
Future Value = Present Value × (1 + (Interest Rate / n))^(nt)
Where:
- Present Value (PV) is the current amount of money, which is $1,708 in this example.
- Interest Rate (r) is the annual interest rate, which is 0.082 (8.2% expressed as a decimal).
- n is the number of times the interest is compounded per year, which is 2 for semiannual compounding.
- t is the number of years the money is invested, which is 15 in this case.
Plugging the values into the formula:
Future Value = $1,708 × (1 + (0.082 / 2))^(2×15)
Future Value = $1,708 × (1 + 0.041)^(30)
Future Value = $1,708 × (1.041)^(30)
Calculating the future value, we find the amount in 15 years with the given interest rate and compounding frequency.