Present value of a series of fixed payments ↩

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created: 2022-02-20 23:09:44
modified: 2022-03-04 16:04:32

• Right now you receive from me a single payment of size
• In return, you will pay me separate unit payments at the end of the years from now

Let the yearly discount factor be in this example. Then what is the sum of the PVs of the fixed payments? In other words, what makes the contract fair?

Solution

Using the multiplicative property of the discount factor:

• The PV of the payment at the end of the year is
• The PV of the payment paid at the end of year is
• The PV of the payment paid at the end of year is

The sum of PVs of all the payments is:

Which in our example is: