How did they get to this answer can someone explain the steps.
Directions: Find the future value of each ordinary annuity, if payments are made and interest is compounded as given.
R = 15,000; 12.1% interest compounded quarterly for 6 yrs.
answer: $518,017.56
I assume R is the quarterly payment, "PYMT"
The number of periods is 6x4 = 24
The interest rate per period is
i = 12.1/4 = 3.025%
Future Value of Annuity
= PMT*[((1 + i)^n - 1) /i]
See http://www.getobjects.com/Components/Finance/TVM/fva.html for more details
To find the future value of an ordinary annuity, we can use the formula:
Future Value of Annuity = PMT * [((1 + i)^n - 1) / i]
In this case, PMT represents the quarterly payment, R, which is $15,000. The number of periods, n, is 6 years, and since interest is compounded quarterly, we multiply the number of years by 4 to get 24 periods.
Next, we need to determine the interest rate per period, i. The given interest rate is 12.1%, which we divide by 4 to get the quarterly interest rate, 3.025%.
Now we can substitute these values into the formula:
Future Value of Annuity = 15000 * [((1 + 0.03025)^24 - 1) / 0.03025]
Using a calculator or spreadsheet, we can calculate the future value:
Future Value of Annuity = $518,017.56
Therefore, the future value of the ordinary annuity with quarterly payments of $15,000, compounded at an interest rate of 12.1% for 6 years, is $518,017.56.