The Multiple Meanings of “Free Cash Flow” Must Know Formulas for Cost Accounting Converting Your Manual Bookkeeping to a Computerized System

# What Happens to an Annuity Deferred?

Deferred annuities are a type of annuity contract that delays payments to the investor until the investor elects to receive them. When the investor is in savings mode, he makes payments into some sort of investment account. The investment grows and compounds in a tax-deferred manner, and the investor pays no taxes on its growth until he decides to convert the investment into an annuity and start receiving regular payments.

You need to understand how to figure the future and present value of a deferred annuity for your intermediate accounting class. The good news is that you use the same method to figure the future value of a deferred annuity as when you calculate the future value of an ordinary annuity.

## Future value of a deferred annuity

In 2013, Penway, Inc., starts planning for a major expansion in 2019. At the end of 2016, 2017, and 2018, Penway reckons that it will be able to invest \$50,000 each year, earning 5 percent annually. How much money will Penway have to play with when it starts its expansion in 2019?

In this example, you have to ignore the first three years (2013, 2014, and 2015) because Penway has no plans to put aside any money during those years. You figure the value accumulated by using the standard formula for a future value of an ordinary annuity.

Checking out the preceding figure, you see that three years at 5 percent gives you a factor of 3.15250. Multiplying that factor by the amount saved per year of \$50,000 gives you the future value of the deferred annuity, which is \$157,625.

## Present value of a deferred annuity

The present value of a deferred annuity tells you how much you need to invest today to achieve your desired savings result in the future. To accomplish this, you use just one different table: the present value of an ordinary annuity of 1.

Put this to work and make it personal! Suppose that you’re 18 years old. As an incentive to stay in school and get good grades, your Aunt Dottie says she’ll give you \$3,000 a year for three years starting five years from now (after your proposed graduation date).

Given an annual interest rate of 5 percent and the total periods (which is seven — four years deferred plus three annual payments), you want to know the present value of the four payments.

Looking at the present value of an ordinary annuity of 1 table in your intermediate accounting textbook or online, you can see that the factor at the intersection of seven periods and 5 percent is 5.78637. Using the same table, you see that the factor at the intersection of four (deferred) periods and 5 percent is 3.54595.