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# Loan Balance Formula

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:

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

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