In this video we discuss how to calculate the present value of an ordinary annuity using the formula. We go through the formula and go through a detailed example
Transcript/notes
The formula to calculate the present value of an ordinary annuity is, present value equals, the payment amount times the quantity, 1 minus, 1 divided by, 1 plus the annual rate divided by the number of compounding periods, raised to the number of compounding periods times the number of years, divided by the annual rate divided by the number of compounding periods.
Here is the formula and a list of the variables.
As an example, let’s say that someone expects to receive an $8000 annuity for the next 3 years. Interest is 8% annually and the payments are received at the end of the year, so this is an ordinary annuity. What is the present value of the annuity?
Plugging into the formula, we have present value equals, $8000 times the quantity, 1 minus, 1 divided by, 1 plus .08, the decimal value of the annual rate divided by 1, the number of compounding periods, raised 1 times 3, the number of years, divided by .08, divided by 1.
I have written all the calculations out on the screen, as you see here, and we get $20,616.78 as the present value of the annuity.
And here is this value checked and explained in detail. At the bottom, we do get a zero value after the payouts.
And here is another example, this time the payments are at the end of each quarter, so n will equal 4. We get a present value of $10,312.12.
Chapters/Timestamps
0:00 Formula to calculate the present value of an ordinary annuity
0:26 Example of how to calculate the present value of an ordinary annuity
1:13 Example checked
1:23 Another example problem