$8,000 in 5 years at a semiannual discount rate of 6%
To calculate the future value of an amount after a certain number of years with a semiannual discount rate, you need to use the formula for compound interest:
Future Value = Present Value * (1 + Semiannual Discount Rate)^n
where:
- Present Value is the initial amount ($8,000 in this case)
- Semiannual Discount Rate is the discount rate per period (6% or 0.06/2 = 0.03 in this case)
- n is the number of periods (5 years * 2 = 10 periods in this case, since we have semiannual compounding)
Using this formula, we can calculate the future value:
Future Value = $8,000 * (1 + 0.03)^10
Future Value = $8,000 * (1.03)^10
Future Value ≈ $8,000 * 1.34392 ≈ $10,751.36
Therefore, $8,000 will accumulate to approximately $10,751.36 after 5 years with a semiannual discount rate of 6%.