Find the present value of an annuity with payments of $600 at the end of every three months for 9 years. The interest rate is 10% compounded quarterly
The present value of the annuity is $ (Round the final answer to the nearest cent as neededRound all intermediate values to six decimal places as needed)
Answer
Round the final answer to the nearest cent: \(\boxed{14133.75}\)
Step 1 ：Given an annuity with payments of $600 at the end of every three months for 9 years. The interest rate is 10% compounded quarterly.
Step 2 ：The present value of an annuity can be calculated using the formula: \(PV = P * [(1 - (1 + r)^{-n}) / r]\) where: \(PV\) is the present value, \(P\) is the payment per period, \(r\) is the interest rate per period, and \(n\) is the number of periods.
Step 3 ：In this case, the payment per period (\(P\)) is $600, the interest rate per period (\(r\)) is 10% per year compounded quarterly (so 10%/4 = 2.5% or 0.025 per quarter), and the number of periods (\(n\)) is 9 years * 4 quarters/year = 36 quarters.
Step 4 ：Substitute these values into the formula: \(P = 600\), \(r = 0.025\), \(n = 36\).
Step 5 ：Calculate the present value: \(PV = 600 * [(1 - (1 + 0.025)^{-36}) / 0.025]\)
Step 6 ：\(PV = 14133.750640772469\)
Step 7 ：Round the final answer to the nearest cent: \(\boxed{14133.75}\)
