Basics of Corporate Finance

As you can see from the table, the interest on the deposit at the end of Year One is compounded for nine years, interest on the deposit at the end of Year Two for eight years, and so forth. The deposit at the end of Year Ten earns no interest. Thus, at the end of ten years, the total future value of this annuity is $1,257.80.

Using a
financial calculator

Most financial calculators can perform this type of calculation. The basic idea is to input the interest rate, the number of payments and the size of the payments, and push the future value key to calculate. Many calculators allow you to specify how many payments per year and whether the payment is made at the beginning of the period (annuity due) or at the end of the period (ordinary annuity).

Present Value of an Annuity

Discounting
annuity payments

The calculation of the present value of an annuity is the reversal of the compounding process for the future value. The idea is to discount each individual payment from the time of its expected receipt to the present. We can illustrate by building another table to calculate the present value of the annuity in Figure 3.4: ten payments of $100, made on December 31st of each year, discounted at a rate of 5%.

Year Payment x PVIF = Present Value
10 $100 x 1/(1.05)10 = 61.39
9 $100 x 1/(1.05)9 = 64.46
8 $100 x 1/(1.05)8 = 67.68
7 $100 x 1/(1.05)7 = 71.07
6 $100 x 1/(1.05)6 = 74.62
5 $100 x 1/(1.05)5 = 78.35
4 $100 x 1/(1.05)4 = 82.27
3 $100 x 1/(1.05)3 = 86.39
2 $100 x 1/(1.05)2 = 90.70
1 $100 x 1/(1.05)1 = 95.24
PV = $772.17

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