numpy.pv()

Compute the present value.

Given:

• a future value, fv
• an interest rate compounded once per period, of which there are
• nper total
• a (fixed) payment, pmt, paid either
• at the beginning (when = {?begin?, 1}) or the end (when = {?end?, 0}) of each period

Return:

the value now

Notes

The present value is computed by solving the equation:

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

or, when rate = 0:

fv + pv + pmt * nper = 0

for pv, which is then returned.

References

Examples

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.

>>> np.pv(0.05/12, 10*12, -100, 15692.93)
-100.00067131625819

By convention, the negative sign represents cash flow out (i.e., money not available today). Thus, to end up with $15,692.93 in 10 years saving $100 a month at 5% annual interest, one?s initial deposit should also be $100.

If any input is array_like, pv returns an array of equal shape. Let?s compare different interest rates in the example above:

>>> a = np.array((0.05, 0.04, 0.03))/12
>>> np.pv(a, 10*12, -100, 15692.93)
array([ -100.00067132,  -649.26771385, -1273.78633713])

So, to end up with the same $15692.93 under the same $100 per month ?savings plan,? for annual interest rates of 4% and 3%, one would need initial investments of $649.27 and $1273.79, respectively.