# Principal of a loan

The principal of a loan is the principal that the debtor receives from the creditor. Interest payable is calculated on this amount.

The principal is one of the central axes of a loan, along with the interest rate, which is the cost of money, and the number of installments. All these elements make it possible to determine the payment schedule.

Each monthly installment has two components: The financial amortization (return of a part of the capital received) and the accrued interest. The latter are calculated by multiplying the interest rate on the loan by the balance of the principal that remains to be paid.

We can see what is explained in the following table for a credit of US \$ 15,000. The monthly interest rate is 3% and six identical monthly installments have been scheduled.

Interests Payment of
principal
Share

Balance

15.000,00
1 450,00 2.318,96 2.768,96 12.681,04
2 380,43 2.388,53 2.768,96 10.292,51
3 308,78 2.460,19 2.768,96 7.832,32
4 234,97 2.533,99 2.768,96 5.298,33
5 158,95 2.610,01 2.768,96 2.688,31
6 80,65 2.688,31 2.768,96
sum 1.613,78 15.000,00 16.613,78

## Repayment of principal on a loan

When structuring the repayment of the principal of a loan, the financial entity normally distributes it in several periods. However, the payment can also be scheduled for a single disbursement.

The latter happens, for example, in the American system of repayment of a loan. The debtor pays the principal in the final installment and during the other periods only pays the interest.

However, the French method is more common, where all the odds are equal. The formula to calculate the monthly payment is as follows:

C = Fee to pay

V = Main

i = Interest rate for the period

## Example of calculating the principal of a loan

Let's look at an example to calculate the principal of a loan. Suppose I have a debt at an interest rate of 1% per month. Assuming there are five installments to pay, each of US \$ 1,236.24. What is the amount of the credit?

Taking as reference the formula of the French method, we can solve the problem:

(1+0,01)^5*0,01 = 0,0105

(1+0,01)^5-1 = 0,051

0,0105/0,051 = 0,206

1.236,24/0,206 = 6.000,01.

So, the principal of the debt is approximately US \$ 6,000.

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