Analogous to the derivation of the present value of an annuity due formula, the future value of an annuity due formula is just the future value of an ordinary annuity formula multiplied by (1 + r):
Using Valuation Tables--The future value of a level annuity due can also be calculated using the tables for the future value of an annuity due contained in Appendix E.
The Pmt for an annuity due given the future value is derived in a manner analogous to the annuity due given the present value by rearranging equation FV4 to solve for Pmt in terms of the other variables.
Number of Periods Present Value Will Provide Annuity Due Payments
Equation N3 calculates the number of periods a given lump sum investment earning some specified periodic rate of return can sustain a specified level of annuity due payments before the fund is exhausted.
Number of Periods of Annuity Due Payments to Reach Future Value
The future value of an inflation-adjusted annuity due can be determined by simply multiplying the future value of the ordinary annuity by (1 + r):
Equation Pmt3' shows the formula for computing the initial payment amount for an inflation-adjusted annuity due based upon a present value:
The formula for the future after-tax value of before-tax annuity due payments is computed simply by multiplying the right-hand side of equation FVAEat1 by (1 + r):
The present before-tax value one needs to invest to generate level after-tax annuity due payments is equal to equation PVAEat1 multiplied by (1 + r):
The formula to determine the present before-tax value one needs to invest in a nondeductible currently fully taxable investment to generate level after-tax annuity due payments is:
The future value before capital gain tax of annuity due payments can be broken into its component parts as follows.