Week 6 Formulas for Annuities

Week 6: Lecture

Formulas For Annuities

So far the formulas we have developed have only dealt with one lump sum to be paid or received at some future time. Suppose, however, you are faced with more than one cash flow, or a whole series of them. In situations like this, the situation is more complicated.

To begin with, if you had multiple cash flows you could use the lump sum formulas for each one and just add up all the present or future values when you were done to get a total. In fact, that's just what you do when cash flows of different amounts are involved (remember that for later).

However, in those situations where you are dealing with a series of equal payments or receipts it is called an annuity. When you are dealing with annuities there are two “short cut” formulas you can use which combine all the separate computations into one step:

Future Value of an Annuity
To find the Future Value of an annuity (that is, the total amount that will have accumulated, including interest, after making payments for a given number of periods n at some percentage rate i):

$FVA=PMT\left[\frac{\left(1+i\right)^n-1}{i}\right]$

Where:	FVA = the Future Value of the Annuity at time n
	PMT = the amount of each payment or receipt

Present Value of an Annuity
To find the Present Value of an annuity (that is the total value today of a stream of payments to be paid or received in the future for a given period of time n at some percentage rate i):

$PVA=PMT\left[\frac{1-\frac{1}{\left(1+i\right)^n}}{i}\right]$

Where:

PVA is the present value of the annuity

Now don't panic; there's an easy way to work these. As before, the terms inside the brackets are called:

Future Value Interest Factor Annuity, FVIFA (for FVA), and
Present Value Interest Factor Annuity, PVIFA (for PVA)

When using the interest factor version of the equations they are written:

FVA=PMT(FVIFA_{i%, n periods}) Future Value of an Annuity Table Download Future Value of an Annuity Table

PVA=PMT(PVIFA_{i%, n periods}) Present Value of an Annuity Table Download Present Value of an Annuity Table