# Compute Loan Balance for a specific month (period) on an amortized loan

I'm looking for is a method that will allow me to compute the Loan Balance value for a specific period (month) in the amortization table without having to compute all of the values before it.

Let's say: your bank loan of 100000\$ at the rate of 10% with annual rate compounded monthly and for a maturity of a 10 years.

So we have following information:

PV = 100000\$, Time (or n) = 10, Frequency (#) = 12 (monthly), Rate (r) = 10% or 0.1.

We should find 66th month Loan Balance value without establishing whole table. Please do not suggest to calculate with Future Value (FV of annuity) formula replacing Time (n) = by 66 (month that we want to find value)

• Why reject an essential part of the only possible solution? Nov 28 '19 at 22:23
• This looks more like a homework problem than an actual personal money problem faced by the OP. Nov 28 '19 at 22:24

Given

``````PV = principal
i  = periodic rate
m  = number of periods
d  = periodic payment

d  = PV i (1 + 1/((1 + i)^m - 1))
``````

the balance `b` remaining in month `x` is

``````b  = (d + (1 + i)^x (i PV - d))/i
``````

``````  PV = 100000
i  = 0.1/12
m  = 10*12

∴ d  = 1321.51

x  =  66
∴ b  =  57276.53
``````

Check: final balance

``````  x  =  120
∴ b  =  0
``````

Formulae

Formula for periodic payment - loan payment formula

Formula for loan balance - inhomogeneous difference equation (Arne Jensen, Aalborg Uni.)