numpy.pv() in Python

numpy.fv(rate, nper, pmt, fv, when = 'end') : This financial function helps user to compute future values. Parameters :

rate : [array_like] Rate of interest as decimal (not per cent) per period nper : [array_like] total compounding periods pmt : [array_like] fixed payment fv : [array_like, optional] future value. Default = 0.0 when : at the beginning (when = {‘begin’, 1}) or the end (when = {‘end’, 0}) of each period. Default is {‘end’, 0}

Return :

present value as per given parameters.

Equation being solved :

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

or when rate == 0

fv + pv + pmt * nper = 0

Code 1 : Working Python

## Python program explaining pv() function

import numpy as np
'''
Question : 

What is the present value (e.g., the initial investment)
of an investment that needs to total $15692.93 after 10
years of saving $100 every month? 
Assume the interest rate is 5% (annually) compounded monthly.
'''

#                 rate        np       pmt   fv
Solution = np.pv(0.05/12, 10*12, -100, 15692.93)

print("present value (fv) : ", Solution)

Output :

present value (fv) :  -100.000671316

Reference : https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.pv.html