ANNUITIES
Series of evenly
spaced, equal payments
Many financial market securities involve more than one cash flow. An annuity is a security with a series of equal payments (or receipts) spaced evenly over a determined period. There are two types of annuities:
Ordinary annuity (also called deferred annuity)
Annuity due
An ordinary annuity payment is received at the end of the payment period, while an annuity due requires payment at the beginning of the period. In this section, we focus on the valuation of ordinary annuities, which are the most common. The calculations for an annuity due are almost the same, but they include an adjustment for the timing of cash payments.
Future Value of an Annuity
Compounding annuity payments
Calculating the future value of an annuity is a fairly straight-forward exercise. However, it can be tedious as the following example illustrates. Suppose that an investor invests $100 each December 31st for the next ten years. The account pays an annual interest rate of 5%. What will be the value of the account at the end of the ten years? Let's build a table that outlines the compounding of the cash flows.
Year Deposit x FVIF = Payments
1 $100 x(1.05)9 = 155.14
2 $100 x (1.05)8 = 147.75
3 $100 x(1.05)7 = 140.71
4 $100 x (1.05)6 = 134.01
5 $100 x (1.05)5 = 127.63
6 $100 x (1.05)4 = 121.55
7 $100 x (1.05)3 = 115.76
8 $100 x (1.05)2 = 110.25
9 $100 x (1.05)1 = 105.00
10 $100 x (1.05)0 = 100.00
FV = $1,257.80