j. Find the PV and the FV of an investment that makes the following end - of - y
ID: 1168053 • Letter: J
Question
j. Find the PV and the FV of an investment that makes the following end - of - year payments. The interest rate is 8%. To find the PV, use the NPV function: PV = Excel does not have a function for the sum of the future values for a set of uneven payments. Therefore, we must find this FV by some other method. Probably the easiest procedure is to simply compound each payment, then sum them, as is done below. Note that since the payments are received at the end of each year, the first payment is compounded for 2 years, the second for 1 year, and the third for 0 years. An alternative procedure for finding the FV would be to find the PV of the series using the NPV function, then compound that amount for 3 years at 8%, as is done below: PV = FV of PV =Explanation / Answer
Interest rate (R) = 8%
Payment in year 1 = $100
Payment in year 2 = $200
Payment in year 3 = $400
Future value at the end of 3 years of above payments = 100*(1+R) ^2 + 200*(1+R) ^1 + 400
Future value at the end of 3 years of above payments =100*1.08^2 + 200*1.08^1 + 400
Future value at the end of 3 years of above payments = $732.64
In another way,
PV of all payment = 100/ (1+R) + 200/ (1+R) ^2 + 400/ (1+R) ^3
PV of all payment =100/1.08 + 200/1.08^2 + 400/1.08^3 = $581.59
FV at the end of 3 years = 581.59*(1+R) ^3
FV at the end of 3 years =581.59*1.08^3 = $732.64 approx.
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