Calculate the value of a deferred annuity at the beginning.
A deferred annuity refers to a series of payments that occurs regularly and consecutively over a certain period of time. With a regular annuity, the payments begin immediately at the end of the first period. In contrast, the payments of a deferred annuity begin at the end of a later period.
Cash Flow
With a deferred annuity, the payments occur consecutively, but they only begin after a certain time from the start of the deferred annuity. For example, assume there are five $100 payments over seven years and the payments begin at the end of the third year. The payments will then occur at the end of the third, fourth, fifth, sixth and seventh years. No cash flow occurs from the beginning of the deferred annuity to the end of the third year.
Present Value Formula for Annuities
Present value of an annuity refers to its value at the beginning of the annuity. To calculate the present value of a deferred annuity, you need to first use the present value formula for a regular annuity, which is as follows: C {[1 - (1 / ((1+i)^n)] / i}. In this formula, C represents the amount of each payment, i stands for interest rate and n stands for the number of payments.
Present Value Calculation for Annuities
You can use the present value formula for regular annuities to calculate the value of a deferred annuity at the beginning of the period when the payments begin. For example, assume again that the deferred annuity has five $100 payments over seven years that begin at the end of the third year and the annual interest rate is 10 percent. You can calculate the value of the deferred annuity at the beginning of the third year as follows: 100 {[1 - (1 / ((1+.10)^5)] / .10} = $379.08.
Present Value of a Deferred Annuity
To obtain the present value of the deferred annuity, you only have to discount the previous figure according to the interest rate and the number of periods before the payments commence. You can do this using this formula: PV [(1/(1+r))^t], where PV represents the value at the beginning of the period when the payments begin and t stands for the number of periods during which there are no payments. Using the same figures as before, you can calculate the present value of the deferred annuity as follows: $379.08 / (1+.10)^2 = $313.29.
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