An annuity is a financial investment that generates regular payments for a set time period. In modern times, an annuity is most often purchased through an insurance company or a financial services company.
Present value and future value are terms that are frequently used in annuity contracts. The present value of an annuity is the sum that must be invested now to guarantee a desired payment in the future, while its future value is the total that will be achieved over time.
An annuity due is an annuity where the payments are made at the beginning of each time period; for an ordinary annuity, payments are made at the end of the time period. Most annuities are ordinary annuities.
Analogous to the future value and present value of a dollar, which is the future value and present value of a lump-sum payment, the future value of an annuity is the value of equally spaced payments at some point in the future. The present value of an annuity is the present value of equally spaced payments in the future.
Present Value of an Annuity
The present value of an annuity is the current value of all the income that will be generated by that investment in the future. In more practical terms, it is the amount of money that would need to be invested today to generate a specific income down the road.
Using the interest rate, desired payment amount, and the number of payments, the present value calculation discounts the value of future payments to determine the contribution necessary to achieve and maintain fixed payments for a set time period.
For example, the present-value formula would be used to determine how much to invest now if you want to guarantee annual payments of $1,000 for 10 years. To achieve a Rs. 1,000 annuity payment for 10 years with interest rates at 8%, you’d need to invest Rs. 6,710.08 today.
Future Value
The future value of an annuity is simply the sum of the future value of each payment. The equation for the future value of an annuity due is the sum of the geometric sequence:
FVAD = A(1 + r)1 + A(1 + r)2 + …+ A(1 + r)n.
The equation for the future value of an ordinary annuity is the sum of the geometric sequence:
FVOA = A(1 + r)0 + A(1 + r)1 + …+ A(1 + r)n-1.
Without going through an extensive derivation, just note that the future value of an annuity is the sum of the geometric sequences shown above, and these sums can be simplified to the following formulas, where
A = the annuity payment or periodic rent,
r = the interest rate per time period,
n = the number of time periods.
