What is the future value of an annuity that has the following characteristics: (a) you pay $1,000.00 per year into the annuity, (b) you make this payment for 10 years, and (c) you are able to obtain a 5% rate of return on your investment.
To calculate the future value of an annuity with the given characteristics, you can use the formula for the future value of an ordinary annuity:
Future Value = Payment x ((1 + Rate)^n - 1) / Rate
Where:
- Payment is the amount you contribute per period
- Rate is the interest rate per period
- n is the number of periods
In this case:
- Payment = $1,000.00
- Rate = 5% or 0.05 (decimal form)
- n = 10 years
Now, let's plug in the values into the formula:
Future Value = $1,000.00 x ((1 + 0.05)^10 - 1) / 0.05
Simplifying this calculation step by step:
Future Value = $1,000.00 x (1.05^10 - 1) / 0.05
Calculator step:
Future Value = $1,000.00 x (1.628894626 - 1) / 0.05
Future Value = $1,000.00 x 0.628894626 / 0.05
Calculator step:
Future Value = $1,000.00 x 12.57789252
Future Value = $12,577.89
So, the future value of the annuity is $12,577.89.