Final answer:
The present value of an ordinary annuity with $7,580 quarterly payments for 6 years at a 10.0% interest rate compounded quarterly is calculated using the present value of annuity formula. This involves using the periodic interest rate of 2.5% and the total number of payment periods (24 quarters).
Step-by-step explanation:
To find the present value of an ordinary annuity with deposits of $7,580 quarterly for 6 years at 10.0% interest compounded quarterly, we use the present value of annuity formula:
PV of Annuity = Pmt × {1 - [1 + (i)]^(-n)} / i
Where:
- Pmt = periodic payment amount ($7,580)
- i = periodic interest rate (10% compounded quarterly is 2.5% per period, or 0.025 as a decimal)
- n = total number of periods (6 years × 4 quarters per year = 24 quarters)
So, we substitute the values to get:
PV of Annuity = $7,580 × {1 - [1 + (0.025)]^(-24)} / 0.025
Performing the calculations, we get the present value of the ordinary annuity. Add up all the present values for the different time periods to get a final answer.