2.3 Future Value of an Ordinary Annuity
An annuity is a series of payments that occur at the same intervals and in the same amounts. An example of an annuity is a series of payments from the buyer of an asset to the seller, where the buyer promises to make a series of regular payments. The formula is:
FVA = PMT [1+rn-1r]
Ordinary annuity: an annuity with payments made at the end of each period.
FVA = the future value of the annuity stream to be paid in the future
PMT = the amount of each annuity payment
r = the interest rate
n = the number of periods over which payments are made
An investor pays equal instalments of R100 at the end of each year into a savings account yielding an interest rate of 12% per year, compounded annually. What is the future value of the investment at the end of three years?
FVA = PMT [1+rn-1r] = R100 [1+ 0.123-10.12] = R100 x 3.3744 = R337.44
We can also use Table B to determine the future value of an ordinary annuity. This table is known as the future value of an annuity of R1 per period and contains the future value interest factor of an annuity (FVIFA). The formula is:
FVA = PMT x FVIFAn;r