Calculate the future ANNUITIES DUE. Round to the nearest cent when necessary.
Annunity Payment:($3,000)Payment Frequency: Every (6) months Time Period Yrs: (5) Nominal Rate%: (10)Interest Compounded: Semiannually Future Value Of The Aunnuity Is What?
To calculate the future value of an annuity due, you can use the formula:
Future Value = Annuity Payment × [(1 + Interest Rate/Nominal Rate)^(Number of Periods/Compounding Frequency) - 1] × (1 + Interest Rate/Nominal Rate)
Given the following information:
Annuity Payment: $3,000
Payment Frequency: Every 6 months
Time Period: 5 years
Nominal Rate: 10% (interest rate)
Interest Compounded: Semiannually
Let's plug in these values into the formula:
Annuity Payment = $3,000
Interest Rate = 10% (or 0.10 in decimal form)
Number of Periods = Time Period × Payment Frequency = 5 years × 2 payments per year = 10 periods
Compounding Frequency = 2 (semiannually)
Future Value = $3,000 × [(1 + 0.10/2)^(10/2) - 1] × (1 + 0.10/2)
Now, let's calculate the future value:
Future Value = $3,000 × [(1 + 0.05)^(5) - 1] × (1 + 0.05)
Using a calculator, we can simplify the formula:
Future Value = $3,000 × (1.27628) × (1.05)
Future Value ≈ $3,831.84
Therefore, the future value of the annuity due is approximately $3,831.84.