### How do I calculate the repayment of a loan?

A loan is a contract whereby one of the parties (which we call a lender) gives money to another (called a borrower). For its part, the borrower agrees to return to the lender all the money borrowed plus interest, setting specific conditions and timeframe.

The repayment of a loan is precisely the process followed by the borrower to return the initial money, plus interest, to the lender.

## How do I calculate the repayment of a loan?

Depending on the type of amortization, it will be done in one way or another. The simplest case is that of a single repayment, in which, at the end of the loan term, we will pay both the initially borrowed money and the interest at one time. Let’s see an example:

In this case, \$ 15,000 has been lent, with an annual interest rate of 6% and a 5-year term to repay the loan. Thus, we can calculate that, in order to repay this loan, we will have to return a total of \$ 20,073.38 at the end of the five years (\$ 15,000 of the money we borrowed at the beginning plus \$ 5,073.38 in interest).

However, the usual process of repayment of a loan and its calculation are more complex, and it is necessary to know all the elements that make it up, to later be able to repay it, that is, to repay it. Go for it! These are the components of a loan:

• Nominal of the loan or principal: Amount of money that they give us when they grant us the loan and that it is necessary to return along with the interests.
• Term of amortization of the period or fee to be paid: Amount of money that must be paid from time to time (as agreed) to gradually return the loan. A portion of this amount will be used to pay interest and another to pay the principal of the loan. Depending on the amortization system we apply, we will devote more or less money to everything.
• Live capital of the period: As we pay the loan installments, the debt we have will decrease. The live capital of the period is the amount we still owe to the lender. That is, it is not all the debt (nominal + interest) but only the part of the nominal that we still have to repay.
• Capital amortized up to a certain period: It is a concept identical to that of living capital but seen from another point of view. If the live capital is the part of the nominal that we have to pay, the amortized capital is precisely the part of the nominal that we have already paid.
• Interest rate for the period: It is the part of the loan installment that we must pay periodically and that is intended to amortize only the interest, not the principal of the loan.
• Period repayment fee: It is the part of the loan installment that we must pay periodically and that is intended only to pay the principal or nominal amount of the loan, not interest. In the case of loans that respond to this scheme, the total amount to be amortized will be the sum of all the amortizing terms or the installments to be paid on the loan.

### Loan amortization tables

All the aforementioned concepts are usually represented within a table called a loan repayment schedule. Although it does not have a fixed structure, and all these components are not always contemplated, the typical form of a depreciation table usually looks similar to this:

## Types of amortization

There is no single amortization system, but there are several options, each with its advantages and disadvantages. In general, the French amortization system is the most frequent in practice and is the one that any financial institution usually applies by default (unless another amortization modality is specified). But what is the French amortization system?

### French amortization system

The French amortization system is characterized by having constant installments. This implies that at the beginning of the amortization we will have to pay more interest and less at the end.

The amortization term, that is, the total amount to be paid in each period, is the same throughout the loan and, therefore, almost everyone chooses to request a loan under this system, since it allows us to more easily manage our finance.

Advantage? That, already in advance, you know how much you have to pay in each period of time (as long as the interest rate does not change, of course).

And how disadvantage? That the principal of the loan does not begin to be amortized, for the most part, until the last loan payments. Let’s see how this method works with an example:

In this example, we see that the borrower has to pay the lender a total of 14,215.73 dollars as an annual fee for the duration of the loan.

A part of that amount will pay the interest generated and the other will be used to return part of the nominal or loan capital. Thus, in the first installment to pay, of the established 14,215.73 dollars, 6,500 (50,000 x 13% interest) will be paid as interest, while the remaining 7,715.73 will be used to amortize the loan capital, with the remaining \$ 50,000 remaining \$ 42,284.27 left to pay.

In the following installment (always \$ 14,215.73), the amount to be paid as interest decreases, since this time it will be \$ 5,496.95 (\$ 42,284.27 x 13% interest rate), leaving \$ 8,718.78 that are deducted from the nominal. Thus, after the second installment, a nominal amount of \$ 33,565.49 will remain.

This process continues for subsequent installments to be paid, as reflected in the table. As we said, in the French system, the fee to be paid is always the same, but, as time goes by, in each of them the amount to pay interest will decrease and the amount dedicated to amortizing capital will increase. At the end of the loan, the lender will have paid the borrower a total of \$ 71,078.65 for having received \$ 50,000 five years ago.

## German amortization method

The German amortization method or method of constant repayment installments is characterized by a constant payment of the nominal amount of the loan, which means that the interest payment will vary each month, being higher at the beginning and lower at the end. This means that the fees to be paid will decrease as time goes by.

The advantage? That every year you take off a proportional part of the nominal amount of the loan or of the capital.

The disadvantage? That, in the first periods of payment, the installments to be paid can be so high that it is difficult to face the payment.

Let’s go with another example!

As we see in this system, the amount of nominal that we amortize each year does not change, since we will always amortize \$ 10,000. Instead, the fees do vary:

• The first installment will be \$ 12,400, of which 10,000 are nominal and \$ 2,400 (30,000 x 8%) of interest.
• In the second installment, as of the \$ 30,000 nominal, we have already removed \$ 10,000, there are only \$ 20,000 left. Therefore, as interest we only have to pay \$ 1,600 (20,000 x 8%). Thus, adding the interest and nominal fee, we will have to pay a total of \$ 11,600 in the second installment.
• In the third and last installment, taking into account that we have already removed another \$ 10,000 from the nominal, as interest we only have to pay \$ 800 (10,000 x 8%), to which we will have to add the \$ 10,000 of nominal that We amortize in each period.

Once all this was done, the loan would be fully repaid having paid a total of \$ 34,800 (the sum of 12,400 + 11,600 + 10,800) for the 30,000 dollars that we initially borrowed under these conditions.
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