Accounting: The Language of Business - Vol. 2 (Intermediate: Part 99)

The market performs miracles so routinely that we take it for granted. Supermarkets provide 30,000 choices at rock-bottom prices. We take it for granted that when we stick a piece of plastic in a wall, cash will come out; that when we give the same plastic to a stranger, he will rent us a car, and the next month, Visa will have the accounting correct to the penny. By contrast, "experts" in government can't even count the vote accurately.

John Stossel

 Accounting and the Time Value of Money (Part L)

by

Charles Lamson

Future Value of an Annuity Due

Future value of annuities due differ from future values of ordinary annuities because the payments occur at the beginning of the period instead of at the end of the period. 

For example, assume that an undergraduate accounting student wants to accumulate a sum of money to pay for a master's program to earn the 150 credit hours required for accounting certification. Rather than investing a single amount today that will grow to a future value, she decides to invest $10,000 a year over the next three years in a savings account paying 10% interest compounded annually. She decides to make the first payment to the bank immediately (specifically, at the end of the year). How much will she have available in her account at the end of 3 years?

Let's compare the annuity due with the ordinary annuity we discussed in Part 96. In part 96, the student made the deposits at the end of each year; thus, the problem was an ordinary annuity. However, if the student makes the payment at the beginning of each year, it is an annuity due.

The timeline depicts a future value for an annuity due with the payments occurring at the beginning of each period. Note that there are three deposits with three compounding periods. that is, each cash flow earns interest. 

Now compare the annuity due to the ordinary annuity depicted below. There are still three deposits, but now there are only two compounding periods. That is, the last deposit does not earn interest. As a result, the future value of an annuity due is more valuable than a future value of an ordinary annuity. 

The timeline for the annuity due indicates that there are three cash flows and all three earn interest for at least one period. We can compute the future value using a series of single sum problems as presented in the following table. 

The accumulated value of the annuity due is therefore $36,410. The difference between the sum of the nominal cash flows ($30,000) and the future value of the future cash flows ($36,410) represents the interest earned on the investment, $6,410.

As with ordinary annuities, solving for a future value of an annuity due as a series of single sum problems is inefficient. Thus, to determine the future value of an annuity due, use a formula table, spreadsheet, or financial calculator. all of which will be discussed in the next few parts. 

*GORDON, RAEDY, SANNELLA, 2019, INTERMEDIATE ACCOUNTING, 2ND ED., PP. 335-336*

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