credits

# formulas of annuity

## Regular Annuity Formulas

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These are the main formulas that are needed to work with regular annuity cash flows (Definition/Tutorial). Please note that these formulas work only on a payment date, not between payment dates. This is the same restriction used (but not stated) in financial calculators and spreadsheet functions.

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height="90" width="80%">$Pmt = \frac{{P{V_A}}}{{\left[ {\frac{{1 - \frac{1}{{{{\left( {1 + i} \right)}^N}}}}}{i}} \right]}}$

Regular Annuity Formulas
To solve for Formula
Future Value $F{V_A} = Pmt\left[ {\frac{{{{\left( {1 + i} \right)}^N} - 1}}{i}} \right]$
Present Value $P{V_A} = Pmt\left[ {\frac{{1 - \frac{1}{{{{\left( {1 + i} \right)}^N}}}}}{i}} \right]$
Periodic Payment
when PV is known
Periodic Payment
when FV is known
$Pmt = \frac{{F{V_A}}}{{\left[ {\frac{{{{\left( {1 + i} \right)}^N} - 1}}{i}} \right]}}$
Number of Periods
when PV is known
$N = \frac{{ - \ln \left( {1 - \frac{{P{V_A}}}{{Pmt}}i} \right)}}{{\ln \left( {1 + i} \right)}}$
Number of Periods
when FV is known
$N = \frac{{\ln \left( {1 + \frac{{F{V_A}}}{{Pmt}}i} \right)}}{{\ln \left( {1 + i} \right)}}$
Discount Rate Can only be calculated through a trial and error process
Variable Definitions
Variable Definition
$$FV$$ Future Value
$$PV$$ Present Value
$$i$$ Discount Rate
$$N$$ Number of Periods
$$Pmt$$ Payment (per period)
$$ln$$ Natural logarithm function (log base e)
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Category: Annuity