How much will you have after five years? How much would you have if you made the deposits at the end of each year?

Because each payment occurs one period earlier with an annuity due, the payments will all earn interest for one additional year. Therefore, the FV of an annuity due will be greater than that of a similar ordinary annuity. If you went through the step-by-step procedure, you would see that our illustrative annuity due has an FV of $331.01 versus $315.25 for the ordinary annuity.
With the formula approach, we first use Equation 2-3, but since each payment occurs one period earlier, we multiply the Equation 2-3 result by (1 I):
FVA due FVAordinary (1 I) (2-4)
FVFVPVPVI/YRI/YRNN PMTPMT
–100053
315.25
End Mode
38 Part 2 Fundamental Concepts in Financial Management

Thus, for the annuity due, FVAdue $315.25(1.05) $331.01, which is the same result as found using the period-by-period approach. With a calculator we input the variables just as we did with the ordinary annuity, but now we set the calculator to Begin Mode to get the answer, $331.01.

Why does an annuity due always have a higher future value than an ordinary annuity?
If you calculated the value of an ordinary annuity, how could you find the value of the corresponding annuity due?
Assume that you plan to buy a condo five years from now, and you need to save for a down payment. You plan to save $2,500 per year, with the first payment made immediately, and you will deposit the funds in a bank account that pays 4 percent. How much will you have after five years? How much would you have if you made the
deposits at the end of each year?

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