Question

7.What is the future value of the annuity if one needs to pay quarterly, the present value is P125,000.00 with an interest rate of 6% compounded monthly, and the total payment of 25?

Answer 1

Solution P 125,000 Present value of annuity Total number of payments Interest rate Step -1: Calculate the quarterly interest rate compounded monthly Quarterly interest rate = {(1 + 6%/12)^3} - 1 = 1.5075125% Step-2: Calculate the Present value annuity factor Present Value annuity factor (excel formula) = PV(1.5075125%,25,-1,,0) = 20.700872 Step-3: Calculate the annuity amount paid quarterly Annuity amount = Present value of annuity / PV factor = P 125,000 / 20.700872 = P 6,038.39 Step 4: Calculate the Future value annuity factor Future Value annuity factor (excel formula) = FV(1.5075125%,25,-1,,0) = 30.091460 Step-5: Calculate the Future value of the annuity Future value = Annuity amount x FV factor = P 6,038.39 / 30.091460 = P 181,704.06 Note: Alternatively, the future value can be calculated directly as under: Future value = P 125,000 x (1 + 6%/12)^(25x3) = P 181,704.07