Present Value of Annuity

Annuity is similar concept to perpetuity, but it is finite. So, payments are either paid or received for a set amount of time. Think about your parents’ mortgage or car loans. You make same payments every single month for a specified number of years.

In order to conceptually understand annuity, we have to play with the perpetuity formula. Check out the graph.

STEP 1:

Here, we calculated perpetuity for year 0, and year 5. They are both $10,000. However, in order to compare apples to apples, we have to discount $10,000 from year 5 to year 0. The difference will be present value of annuity.

STEP 2:

So, pretty much what we did is we took payments of $500 forever from year 0, and payments of $500 forever from year 5. If you subtract all payments of $500 forever from year 5, than you’re left over only with payments from years 1 through 5. Therefore, the formula for PV of annuity is: