The Loan Balance formula is a handy tool for anyone needing to calculate the remaining balance of a loan, taking into account the current payment, interest, and term remaining. This is commonly used by banks and financial institutions who provide loans with manageable repayment options known as equated monthly installments. These installments are set in a way that it doesn't strain the borrower's pocket while also covering the interest.
Here is the loan balance formula,
\(\begin{array}{l}B=A(1+r)^n-\frac{p}{r}[(1+r)^n -1]\end{array} \)
Where,
B = Balance Amount
A = Loan Amount
P = Payment Amount
r = Rate of Interest (compounded)
n = Number of time periods
Examples for better understanding
Example:
Calculate the remaining loan balance after 2 years if the initial loan amount is Rs 200000, the monthly payment amount is Rs 1800, and the annual interest rate is 5%.
Solution:
Given Original loan amount A = 200000
B = Balance Amount
P = 1800
r =5/1200 = 0.0042
n = 02 years = 24 months
Applying the loan formula:
\(\begin{array}{l}B=A(1+r)^n-\frac{p}{r}[(1+r)^n -1]\end{array} \)
\(\begin{array}{l}B=200000(1+0.0042)^{24}-\frac{1800}{0.0042}[(1+0.0042)^{24} -1]\\ =200000\times 1.1033-428571.43(1.1033-1)\\ =220660-47402.9\\ =173257.10\end{array} \)
