How to Calculate a Loan Amount Based on a Payment

The principal of a loan is the initial amount of the loan, and the interest on the loan is an additional amount that the lender charges you for the loan. You will generally repay the loan by making fixed payments at regular intervals. You can calculate the loan's principal from the interest rate, number of payments and the amount of each payment.

Interest

Calculate the interest rate for the payment interval. Assume the annual interest rate on the loan is 9 percent. Divide this interest percentage by 100 to get a decimal number of 0.09. Divide this rate by the number of loan payments in a year. Assume this loan requires monthly payments, giving you a monthly interest rate of 0.09 / 12 = 0.0075.

Payments

Multiply the term of the loan in years by the number of payments in a year. Assume the term of the loan in this example is 10 years. This loan requires 10 x 12 = 120 payments to repay the loan.

Payment Amount

Determine the payment amount. You typically want to make the largest payment you can afford, to minimize the interest that you pay. Assume for this example that you can afford to make a payment of $200 each month.

Loan Amount

Compute the loan amount with the formula A = (P / i) x [1 ' (1 + i)^-N]. A is the loan amount, P is the payment, i is the interest and N is the number of payments to make. The amount of the loan is therefore (200 / 0.0075) x [1 ' (1 + 0.0075)^-120] = 15,788.33 dollars.