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Example: Calculate the present value of a series of $2,000 annual payments to be made at the end of each year for the next four years, assuming a discount rate of 5% (an ordinary annuity is a series of equal payments made at the end of each period).
Therefore, the simple formula for the present value of an n-period annuity due is just the simple formula for the present value of an n-period ordinary annuity (equation PV7) multiplied by (1 + r), or:
The future value calculation of an ordinary annuity can be derived directly from the formula for the present value of an ordinary annuity by substituting the present value of a lump sum formula for PV into the present value of the formula for an ordinary annuity and solving for FV.
Multiply both sides of the equation by [(1 + r).sup.n] and one gets the formula for the future value of an ordinary annuity:
[Using Valuation Tables--The future value of a level ordinary annuity due can also be calculated using the tables for the future value of an ordinary annuity contained in Appendix F.
The future value of an inflation-adjusted ordinary annuity is:
Equation Pmtl' shows the formula for computing the initial payment amount for an inflation-adjusted ordinary annuity based upon a given present value:
The formula to determine the present before-tax value one needs to invest in a tax-deductible, tax-deferred plan to generate after-tax ordinary annuity payments is:
This is the present value of an ordinary annuity. When the YTM is known, the present value of an ordinary annuity formula can be used on any interest payment date after the payment has been made to find the present value of the remaining coupon payments.