Future Value (FV)

fv(rate, nper, pmt, pv[, when])

Compute the future value.

syse.fv(rate, nper, pmt, pv, when='end')

Compute the future value.

  • a present value, pv

  • 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


the value at the end of the nper periods

  • rate (scalar or array_like of shape(M, )) – Rate of interest as decimal (not per cent) per period

  • nper (scalar or array_like of shape(M, )) – Number of compounding periods

  • pmt (scalar or array_like of shape(M, )) – Payment

  • pv (scalar or array_like of shape(M, )) – Present value

  • when ({{'begin', 1}, {'end', 0}}, {string, int}, optional) – When payments are due (‘begin’ (1) or ‘end’ (0)). Defaults to {‘end’, 0}.


Future values. If all input is scalar, returns a scalar float. If any input is array_like, returns future values for each input element. If multiple inputs are array_like, they all must have the same shape.

Return type:



The future 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

Example 1:

You invest $20,000 in a retirement account and expect to earn a 10% annual return. How much do you expect to be in the account after 20 years?

import numpy as np
import syse as syse

account_value = syse.fv(0.1,20,0,20000)

print(f"Account Value = ${abs(account_value):,.2f}")

Account Value = $134,550.00

Example 2:

You are planning for your retirement and will be investing $250/month into an IRA. You expect a monthly return of 1% and are 45 years from your expected retirement date. Given this information, how much do you expect to be in your retirement account when you retire?

import numpy as np
import syse as syse

ira_value = syse.fv(0.01,12*45,250,0)

print(f"IRA Value = ${abs(Q5):,.2f}")

IRA Value = $5,363,673.26

Video for Example 1:

Video for Example 2: