You are scheduled to receive annual payments of $9,500 for each of the next 20 y

Question

You are scheduled to receive annual payments of $9,500 for each of the next 20 years. Your discount rate is 10 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?

You are scheduled to receive annual payments of $9,500 for each of the next 20 years. Your discount rate is 10 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?

Explanation / Answer

The present value in the both the cases can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Discount Rate, Nper = Period, PMT = Payment and FV = Future Value (if any). This function is to be used when payments occur at the end of the year.

When payments occur at the beginning of the year, the PV function would be PV(Rate,Nper,PMT,FV,Type) where Type indicates annuity due.

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Step 1: Calculate Present Value when Payments Occur at End of the Year

Here, Rate = 10%, Nper = 20, PMT = $9,500 and FV = 0

Using these values in the above formula for PV, we get,

Present Value = PV(10%,20,9500,0) = $80,878.86

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Step 2: Calculate Present Value when Payments Occur at Beginning of the Year

Here, Rate = 10%, Nper = 20, PMT = $9,500 FV = 0 and Type = 1

Using these values in the above formula for PV, we get,

Present Value = PV(10%,20,9500,0,1) = $88,966.74

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Step 2: Calculate the Difference in Present Value

Difference = 88,966.74 - 80,878.86 = $8,087.89 (answer)

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