In this video we discuss how to calculate the present value of an annuity due by hand using the formula. We go through a couple of examples showing all of the steps
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, time the quantity, 1 plus 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 payments of $500 at the beginning of each quarter for the next 6 years. Interest is 5% annually. Since the payments are received at the beginning, this is an annuity due. What is the present value of the annuity?
Plugging into the formula, we have present value equals, $500 times the quantity, 1 minus, 1 divided by, 1 plus .05, the decimal value of the annual rate divided by 4, the number of compounding periods, raised 4 times 6, the number of years, divided by .05, divided by 4.
I have written all the calculations out on the screen, as you see here, and we get $10,441.02 as the present value of the annuity.
And here is another example, this time the payments are at the beginning of each year for 3 years, so n will equal 1. We get a present value of $22,266.12.
Chapters/Timestamps
0:00 Formula to calculate the present value of an annuity due
0:30 Example of how to calculate the present value of an annuity due
1:25 Example 2