How to calculate loan balance formula?

How to Calculate Loan Balance Formula

Determining the remaining balance of a loan requires a calculation that takes into account the initial principal borrowed, the periodic payment made, the interest rate, and the number of payments already completed. This calculation incorporates the compounding effect of interest on the unpaid principal.

Loan Balance Formula:

Loan Balance = P * ( (1 + r/n)^(n*t) - (1 + r/n)^(n*(t-m)) ) / ( (1 + r/n)^(n*t) - 1)

Where:

• P is the initial principal amount borrowed.
• r is the annual interest rate (expressed as a decimal).
• n is the number of payment periods per year.
• t is the total number of payment periods for the loan term.
• m is the number of payment periods that have already been made.

Steps to Calculate Loan Balance:

1. Convert the annual interest rate to a monthly rate: r / n
2. Multiply the monthly interest rate by the number of payment periods per year: (r / n) * t
3. Determine the exponential term: (1 + r/n)^(n*t)
4. Multiply by the initial principal: P (1 + r/n)^(nt)
5. Calculate the exponential term for the number of payments made: (1 + r/n)^(n*(t-m))
6. Subtract the exponential term in step 5 from the exponential term in step 4: (1 + r/n)^(nt) – (1 + r/n)^(n(t-m))
7. Multiply by the division of step 4 and 6: (P (1 + r/n)^(nt)) / ( (1 + r/n)^(n*t) – 1)

Example:

Suppose you have a loan with the following details:

• Initial principal: $10,000
• Annual interest rate: 5%
• Number of payment periods per year: 12
• Number of payments made: 6
• Loan term: 60 months (5 years)

Using the loan balance formula, we can calculate the remaining balance as follows:

Loan Balance = 10,000 * ( (1 + 0.05/12)^(12*5) - (1 + 0.05/12)^(12*(5-6)) ) / ( (1 + 0.05/12)^(12*5) - 1)
= $9,238.42

Therefore, the remaining balance on the loan after 6 payments of $191.67 is $9,238.42.