To know the Loan Balance, including the current payment, interest and term remaining – Loan balance calculator is used. To know the amount remaining to be repaid by the borrower in a certain time, then the Loan Balance formula is used. The banks provide a loan with easy repayment option that is called the equated monthly instalments. Equated monthly instalments are devised in such a way that the borrowers pays back to the lender (banks/financial institutions etc) without being heavy for the pocket and the interests is also taken care of.

Find loan balance formula below,

\(B=A(1+r)^n-\frac{p}{r}[(1+r)^n -1]\)

Where,

B = Balance Amount

A = Loan Amount

P = Payment Amount

r = Rate of Interest (compounded)

n = Number of time periods

### Solved Examples

**Question:**

Find the balance loan after 1 year, when the original loan amount is Rs 100000, the monthly payment amount is Rs 900 and the annual interest rate of 4%.

**Solution: **

Given Original loan amount A = 100000

B = Balance Amount

P = 900

r =4/1200 = 0.0033

n = 01 years = 12 months

Using the loan formula:

\(B=A(1+r)^n-\frac{p}{r}[(1+r)^n -1]\)

\(B=100000(1+0.0033)^{12}-\frac{900}{0.0033}[(1+0.0033)^{12} -1]\\ =100000\times 1.0403-272727.27(1.0404-1)\\ =104030-10990.9\\ =93011.81\)