Annuity Calculations

Overview¶

This article explains various means of calculating the payment amount of an annuity given the present value and interest rate.

IMPORTANT NOTE REGARDING INTEREST RATES AND APR

1. In the following formulas, the interest rate is the PERIODIC rate. Thus, if N is in months, then the interest rate should be PER MONTH.

2. Banks typically calculate APR as COMPOUNDED YEARLY. Thus if N is in months, then the interest rate you use should be APR/12.

Solutions¶

In Excel¶

Annuity Calculation in Excel

In Visual Basic¶

Function AnnuityToPvRatio(i As Double, N As Integer) As Double

    Dim fp As Double
    fp = FutureToPvRatio(i, N)
    
    AnnuityToPvRatio = (i * fp) / (fp - 1)

End Function
Function FutureToPvRatio(i As Double, N As Integer) As Double

    FutureToPvRatio = (1 + i) ^ N

End Function

Manual Calculation¶

         i (1+i)^N     
A/P = ---------------    
        (1+i)^N - 1


         i (F/P)      
     = -------------    
        (F/P) - 1

        
Solving for N,

     -log(1 - PI/A)
N = ----------------
       log(1 + I)

SQL Server Function¶

create or alter function dbo.AnnuityPaymentQty(
     @apr decimal(20,10) 
    ,@p   decimal(20,10) 
    ,@a   decimal(20,10) 
) returns int as begin

/*-------------------------------------*/
/*
declare
     @apr decimal(20,10) = 0.08
    ,@p   decimal(20,10) = 10000
    ,@a   decimal(20,10) = 202.76
    -- Expected result: 60
*/
/*-------------------------------------*/
declare @interest decimal(20,10) = @apr / 12.0

declare @n int = -log(1-(@p*@interest/@a)) / log(1 + @interest)

return @n

end