Final answer:
To find the present value of an annuity with quarterly payments of $1,000 for 10 years at a 4% interest rate compounded quarterly, apply the present value of an annuity formula. Calculate it by multiplying the periodic payment by the factor that accounts for the discounted value of each payment received in the future.
Step-by-step explanation:
When calculating the present value of an annuity with quarterly payments of $1,000 for 10 years, and a quarterly interest rate of 4%, the following annuity formula is used:
Present Value of Annuity = P × [(1 - (1 + r)^{-n}) / r]
Where P is the periodic payment amount, r is the periodic interest rate, and n is the total number of payments. Quarterly payments for 10 years mean n equals 40 payments (4 quarters × 10 years). The interest rate of 4% compounded quarterly becomes r equals 0.01 (4% per year equals 1% per quarter)
Substituting these values into the formula, we get:
Present Value of Annuity = $1,000 × [(1 - (1 + 0.01)^{-40}) / 0.01]
Performing the calculations will give you the present value of the annuity.