# AP-101

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The present value of a future payment F_T at time T answers the question “How much would need to be deposited in a bank account today in order to have a balance equal to F_T at that date?”

At an interest rate of r, an initial deposit of X dollars will grow over time as shown below.

 Date Balance 0 X 1 X+rX=X(1+r) 2 [X(1+r)](1+r)=X(1+r)^2 3 X(1+r)^3 ... ... T X(1+r)^T

In order to have the target amount, F_T at T, the deposit X would need to satisfy the equation:

X(1+r)^T=F_T

Solving that for X gives the fundamental formula used in present value calculations:

X=(F_T)/(1+r)^T

URL: https://cleanenergyfutures.insightworks.com/pages/4817.html
Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 04/20/2019