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# Annuity Formula

We have already derived the annuity formula that relates the present value to the future stream of payments. This calculation involves knowing or estimating the risk-free interest rate, as well as the time period, the number and amount of each payment. Here we present two online calculators that implement the formulas and calculate the annuity due for your convenience. You should also visit our 'how it works' page to learn more about payday loans.

Present Value Calculator

The following calculator is able to calculate the present value (or the fair value) of an annuity given the monthly income, the term length (in number of months), and the interest rate. The interest rate is either the long-term prevailing interest rate reflected in U.S. Treasury bonds or the annuity rate offered by the insurance rate. Both are probably fairly close. Use this calculator when you know what kind of income stream you would like, but want to calculate its present value (or fair value) so you can compare it to another income stream (with different terms). You can also use it to calculate the immediate value of your annuity in the event that you would like to see it.

Income Calculator (For Annuity Due)

The income calculator supposes that you have saved some large amount of money and are ready to put it into an annuity. The calculator figures out what kind of income stream you can get if you specify the total amount of money you have saved for putting into the fund, the interest rate (or annuity rate), and the length of the contract in terms of the number of months. Each month is assumed to equal one income or payment cycle.

How The Calculator Works Under The Hood

The calculator makes use of the full present value formula. We show a derivation of the formula using elementary mathematics. The way an annuity is priced is through its present value, i.e. converting the stream of future payments into a lump sum in the present.