James has set up an ordinary annuity to save for his retirement in 18 years. If his monthly payments are $225 and the annuity has an annual interest rate of 8% compounded monthly, what will be the value of the annuity when he retires?
i = .08/12 = .006666..
n = 18(12) = 216
amount = 225( 1.00666..^216 - 1)/.00666..
= ...
you do the button pushing
thanks...I got it!
To find the value of the annuity when James retires, we need to calculate the future value of his monthly payments.
First, let's calculate the number of monthly payments James will make over 18 years:
Number of monthly payments = 18 years * 12 months/year = 216 months
Now, let's calculate the future value of the annuity using the formula for the future value of an ordinary annuity:
Future Value = Payment Amount x ((1 + Interest Rate)^Number of Payments - 1) / Interest Rate
Plug in the given values:
Payment Amount = $225
Interest Rate = 8% per year = 8%/12 months = 0.08/12 = 0.006667 (monthly interest rate)
Number of Payments = 216 months
Future Value = $225 x ((1 + 0.006667)^216 - 1) / 0.006667
Now, let's calculate this value using a financial calculator, spreadsheet software, or an online annuity calculator. The result should be approximately $93,193.24.
Therefore, the value of the annuity when James retires will be approximately $93,193.24.