How to calculate time value of money with Python for Business and Finance analysis.

All required TVM calculations can be easily realised with Python.

Future Value (FV) - Compounding formula:

𝐹𝑉 = 𝑃𝑉(1 + 𝑟)^n

Where:

FV: Future Value
PV: Present Value (today)
r: Interest Rate (per period)
n: number of periods

PV = 100 
r = 0.05 
n = 3
FV = PV * (1 + r)**n

You can also calculate FV using NUMPY library which is much more simple way to do it.

import numpy as np
import numpy_financial as npf

PV = 0
cf = -2000
r = 0.03
n = 25

FV = npf.fv(rate = r, nper = n, pmt = cf, pv = PV)
FV

Present Value (PV) - Discounting formula:

𝑃𝑉 = 𝐹𝑉 / (1 + 𝑟)^𝑛

Where:

FV: Future Value
PV: Present Value (today)
r: Interest Rate (per period)
n: number of periods

FV = 20000
n = 4
r = 0.045
PV = FV / (1 + r)**n

You can also calculate PV using NUMPY library which is much more simple way to do it.

import numpy as np
import numpy_financial as npf

FV = 20000
r = 0.03
n = 25
cf = 5000

PV = npf.pv(rate = r, nper = n, pmt = cf, fv = FV)
PV 

Interest Rates formula:

𝑟 = ( 𝐹𝑉/𝑃𝑉) ^ 1/𝑛 − 1

Where:

FV: Future Value
PV: Present Value (today)
r: Interest Rate (per period)
n: number of periods

pv = 10000
fv = 15000
n = 10
r = (fv / pv)**(1/n) - 1

Stock Returns (Price Return) formula:

𝑟 = 𝑃𝑡+1/𝑃𝑡 − 1

Where:

Pt: Price @ timestamp t
Pt+1: Price @ t+1
r: Period Return (Price Return)

p0 = 976
p1 = 1053
p_ret = p1 / p0 - 1

Stock Returns (Total Return = Price Return + Dividend Yield) formula:

𝑟 = (𝑃𝑡+1 + 𝐷𝑡+1) / 𝑃𝑡 − 1 = 𝑃𝑡+1 / 𝑃𝑡 − 1 + 𝐷𝑡+1 / 𝑃𝑡

Where:

Pt: Price @ timestamp t
Pt+1: Price @ t+1
Dt+1: Dividend payment @ t+1
r: Period Return (Total Return)

div = 40
div_y = div / p0
total_ret = p_ret + div_y

See also related topics: