# Present Value of an Annuity

The present value of an annuity shows you the single sum you need to invest at compound interest now in order to provide a series of payments back to you in the future. Sound like the type of information you want to have to plan your retirement?

To mix this up a little bit, here are typical homework and test questions that you may encounter in your intermediate accounting class, which will help to illustrate how to figure out the present value of an ordinary annuity and an annuity due.

## Present value of an ordinary annuity

Just to refresh your memory, don’t forget that, with an ordinary annuity, payment occurs at the end of each period instead of at the beginning. So imagine that your financial accounting instructor has the following question on the midterm — how do you calculate the correct answer?

“What is the present value of nine annual cash payments of $10,000, to be paid at the end of each year using an interest rate of 6 percent?” You know that this is an annuity because the amount of the payment and the interval between payments is the same year after year.

And at this point, you probably have a hint that you have to use either a table or a financial calculator. But what table? Gasp! You use the present value of an ordinary annuity of 1 table.

At this point, you’re probably a pro at reading the tables, so included is the only relevant line from the table for this illustration. Using the factor from the following figure, your answer is $68,017 ($10,000 x 6.8017).

## Present value of an annuity due

Just like the future value of annuities due, the present value of an annuity due calculates annuities taking place sooner — that is, at the beginning instead of end of the period.

The following is a typical homework assignment or test question you may see in your intermediate accounting class:

“Penway, Inc., rents equipment for nine years, with annual rent payments of $15,000 to be made at the beginning of each year. Compounding interest at a rate of 6 percent, what is the present value of the lease obligation?”

Checking out the preceding figure, you see that the factor is 6.8017. Just like with the future value of an annuity due, you have to consider an additional factor of 1 plus the interest rate. So you multiply 1.06 times 6.8017 to get the present value of an annuity due, which is 7.2098. Your answer to the question is $108,147.03 ($15,000 x 7.2098).

Your intermediate accounting textbook may contain a table for the present value of an annuity due of 1. If it does, you don’t have to go through the extra work of computing the annuity due factor. In that table, at the intersection of nine periods and 6 percent, you’ll find the same 7.2098.