PMTGA
Updated: 07 February 2011
Use PMTGA to calculate the initial payment for a growing annuity, given the future value. The formula for the calculation of the initial payment of a growing annuity is:
Syntax
SELECT [wctFinancial].[wct].[PMTGA](
<@FV, float,>
,<@Pgr, float,>
,<@Nper, int,>
,<@Rate, float,>
,<@Pay_type, int,>)
Arguments
@FV
the future value of the annuity. @FV is an expression of type float or of a type that can be implicitly converted to float.
@Pgr
the periodic growth rate of the annuity. This is the percentage amount, expressed as a decimal, by which the annuity will increase in each period. @Pgr is an expression of type float or of a type that can be implicitly converted to float.
@Nper
the number of annuity payments. @Nper is an expression of type float or of a type that can be implicitly converted to float.
@Rate
the percentage rate of return, expressed as a decimal, that you expect the annuity to earn over the number of periods. The annuity payments are compounded using this value. @Rate is an expression of type float or of a type that can be implicitly converted to float.
@Pay_type
the number 0 or 1 and indicates when payments are due. @Pay_type is an expression of type int or of a type that can be implicitly converted to int. If @Pay_type is not 0 it is assumed to be 1.
Set @Pay_type equal to

If payments are due

0

At the end of a period

1

At the beginning of a period

Return Type
float
Remarks
Â· The PMTGA value will have the same sign as @FV.
Â· If the @Pay_type is not equal to zero, it is assumed to be 1.
Â· To calculate the Future value of a growing annuity, use the FVGA function.
Examples
Letâ€™s say you are going to work for 40 more years, and you would like to have a million dollars in your taxdeferred account after 40 years. Assuming that you can increase your contributions by 3% per year and that your taxdeferred account will earn 7% per year, what is the initial (annual) payment to be made into the annuity?
SELECT
wct.PMTGA(1000000 @FV
,.03 @Pgr
,40 @Nper
,.07 @Rate
,1 @Pay_type
) as PMT
This produces the following result.
PMT

3191.75519827819
(1 row(s) affected)
We can verify this calculation by using the FVGA function.
SELECT wct.FVGA(3191.75519827819,.03,40,.07,1) as FVGA
This produces the following result.
FVGA

1000000
(1 row(s) affected)