numpy.pmt¶

numpy.pmt(rate,nper,pv,fv=0,when='end')[source]¶

Compute the payment against loan principal plus interest.

Given:

• a present value,pv (e.g., an amount borrowed)
• a future value,fv (e.g., 0)
• an interestrate compounded once per period, of whichthere are
• nper total
• and (optional) specification of whether payment is madeat the beginning (when = {‘begin’, 1}) or the end(when = {‘end’, 0}) of each period

Return:

the (fixed) periodic payment.

Parameters:	rate : array_like Rate of interest (per period) nper : array_like Number of compounding periods pv : array_like Present value fv : array_like, optional Future value (default = 0) when : {{‘begin’, 1}, {‘end’, 0}}, {string, int} When payments are due (‘begin’ (1) or ‘end’ (0))
Returns:	out : ndarray Payment against loan plus interest. If all input is scalar, returns ascalar float. If any input is array_like, returns payment for eachinput element. If multiple inputs are array_like, they all must havethe same shape.

Notes

The payment is computed by solving the equation:

fv+pv*(1+rate)**nper+pmt*(1+rate*when)/rate*((1+rate)**nper-1)==0

or, whenrate==0:

fv+pv+pmt*nper==0

forpmt.

Note that computing a monthly mortgage payment is onlyone use for this function. For example, pmt returns theperiodic deposit one must make to achieve a specifiedfuture balance given an initial deposit, a fixed,periodically compounded interest rate, and the totalnumber of periods.

References

[WRW]

Wheeler, D. A., E. Rathke, and R. Weir (Eds.) (2009, May).Open Document Format for Office Applications (OpenDocument)v1.2,Part 2: Recalculated Formula (OpenFormula) Format - Annotated Version,Pre-Draft 12. Organization for the Advancement of Structured InformationStandards (OASIS). Billerica, MA, USA. [ODT Document].Available:http://www.oasis-open.org/committees/documents.php?wg_abbrev=office-formulaOpenDocument-formula-20090508.odt

Examples

What is the monthly payment needed to pay off a $200,000 loan in 15years at an annual interest rate of 7.5%?

>>>np.pmt(0.075/12,12*15,200000)-1854.0247200054619

In order to pay-off (i.e., have a future-value of 0) the $200,000 obtainedtoday, a monthly payment of $1,854.02 would be required. Note that thisexample illustrates usage offv having a default value of 0.