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> Initial balance(given balance after k payments,balance index,period payment and period rate)
Initial balance(given balance after k payments,balance index,period payment and period rate)
Formula
B0
initial balance (loan principal)
Bk
balance after k payments
r
period rate for monthly payments
p
period (monthly) payment
k
balance index
Formula description
The balance of a loan by repeated substitution.
Calculator (
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Bk
r
%, percent,parts per hundred
decimal
‰, per mil,parts per thousand,per mille,permil,permille,per mill,promille
permyriad,basis point,bp,percentage in point,pip,parts per ten thousand,one-hundredth percent
parts per million,ppm
parts per billion,ppb
parts per trillion,ppt
parts per quadrillion,ppq
p
k
B0
Precision
0
1
2
3
4
5
6
7
8
9
Formula code
C
C#
C++
Java
JavaScript
LaTeX
PHP
#include
B0 = (Bk + (pow(1+r,k)-1)*p/r)/pow(1+r,k)
B0 = (Bk + (Math.Pow(1+r,k)-1)*p/r)/Math.Pow(1+r,k)
#include
B0 = (Bk + (pow(1+r,k)-1)*p/r)/pow(1+r,k)
B0 = (Bk + (Math.pow(1+r,k)-1)*p/r)/Math.pow(1+r,k)
B0 = (Bk + (Math.pow(1+r,k)-1)*p/r)/Math.pow(1+r,k)
B_0 = \frac{B_k + \frac{(1+r)^k-1}{r} p}{(1+r)^k}
$B0 = ($Bk + (pow(1+$r,$k)-1)*$p/$r)/pow(1+$r,$k)
References
Wikepedia:Formulae.
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