Calculate the future of the following Ordinary Annuities. Round to the Nearest cent when necessary. Annunity Payment ($3,000) Payment Frequency Every (6) Months Time Period (years) 10 Interest Compounded (Semiannually) Future Value Of The Annuity is What?
Annuity Payment ($100) Payment Frequency Every Month Time Period (Years) 12 (Monthly) Future Value Of The Annuity is What?
To calculate the future value of an annuity, we can use the formula:
Future Value = Payment Amount * [(1 + Interest Rate)^n - 1] / Interest Rate
Where:
- Payment Amount is the amount of each annuity payment
- Interest Rate is the interest rate per compounding period
- n is the total number of compounding periods
For the first annuity with a payment of $3,000, payment frequency of every 6 months, a time period of 10 years, and interest compounded semiannually, we can fill in the values:
Payment Amount = $3,000
Interest Rate = 0.08 (assuming an 8% interest rate)
n = 10 * 2 (since there are 2 compounding periods per year)
Future Value = $3,000 * [(1 + 0.08/2)^(10*2) - 1] / (0.08/2)
Simplifying the equation, we have:
Future Value = $3,000 * [(1.04)^20 - 1] / 0.04
Now we can calculate the future value using a calculator:
Future Value = $3,000 * (2.208) / 0.04 ≈ $165,600
So, the future value of the first annuity is approximately $165,600.
For the second annuity with a payment of $100, payment frequency every month, a time period of 12 years, and interest compounded monthly, we can follow the same steps:
Payment Amount = $100
Interest Rate = 0.08 (assuming an 8% interest rate)
n = 12 * 12 (since there are 12 compounding periods per year)
Future Value = $100 * [(1 + 0.08/12)^(12*12) - 1] / (0.08/12)
Simplifying the equation, we have:
Future Value = $100 * [(1.00667)^144 - 1] / 0.00667
Calculating the future value using a calculator:
Future Value = $100 * (1.8113) / 0.00667 ≈ $273,420
So, the future value of the second annuity is approximately $273,420.