numpy.pv¶
- numpy.pv(rate, nper, pmt, fv=0.0, when='end')[source]¶
Compute the present value.
- Given:
- Return:
- the value now
Parameters: rate : array_like
Rate of interest (per period)
nper : array_like
Number of compounding periods
pmt : array_like
Payment
fv : array_like, optional
Future value
when : {{‘begin’, 1}, {‘end’, 0}}, {string, int}, optional
When payments are due (‘begin’ (1) or ‘end’ (0))
Returns: out : ndarray, float
Present value of a series of payments or investments.
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
[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 Information Standards (OASIS). Billerica, MA, USA. [ODT Document]. Available: http://www.oasis-open.org/committees/documents.php?wg_abbrev=office-formula OpenDocument-formula-20090508.odt 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.