# How your loan monthly payments are calculated

## Understanding what’s behind the bank rate.

Last day, I came across a post talking about how someone who took a mortgage loan is now suffering to repay his monthly payments because it’s been 15 years now and he didn’t understand the first time the rate he had. And I had this question in my mind: What does the percentage that the bank gives you mean? So I decided to truly understand what’s behind the scene and to know how formulas are created for this topic.

# What’s a credit and interest rate ?

A credit is a loan that allows you to finance a project, this project can be a home or a real estate and it’s called mortgage or it can be a good or a service and its called consumer credit. In both cases, the borrower agrees to pay back every period in a known time. In the other hand, an interest rate is an amount that you pay for the entity or person who lends you money, and it’s usually a proportion of the amount lent. For example if you borrow 100$ with an interest of 5% one time, you’re going to pay 105$ to the lender. His remuneration will be then 5$. The value of the different rates are generally regulated by the law.

# How monthly payments are calculated ?

The monthly repayment of your loan will depend on the amount borrowed, the duration of your loan (and therefore the number of monthly payments) as well as the periodic rate.

## From annual rate to periodic one

When your loan submission is approved, the entity that lends you the desired amount informs you about the annual percentage rate of charge (which includes the interest rate, insurance, and any costs related to the loan such as administration fees) which will be applied to your loan.

However, you don’t pay off your credit once every year. In most cases, the loan is repaid monthly. It is therefore necessary to change the periodicity of the rate. When we repay once a year, we use the annual rate to calculate the interest, when we repay once a month, it is a monthly rate, and we need a quarterly rate if we’re repaying every three months. We call that a periodic rate, which means a rate that corresponds to the frequency of repayments.

To know the exact periodic rate that’s gonna be applied on your loan, we do the math:

## What are the components of your monthly payment ?

When your bank confirm your loan, you pay off a certain pre-determined amount each month. This amount corresponds to the repayment of a part of the borrowed capital, but also to the repayment of interests.

Interests are calculated each period on the remaining capital. In other words, the more you pay back, the lower the interests are. So, at the start of your repayments, the monthly payments are largely the repayment of interest, and at the end of the credit period, the monthly payments are largely the repayment of the borrowed capital.

In fact, for the first repayment period, you pay your monthly payment with the interest that applies to the entire borrowed capital. In the second period, interest is charged on the principal borrowed minus the capital returned in the first period. The amount of interest is therefore lower in the second than in the first period. And so on for next periods.

Let’s take this example to understand more. You got a loan of 1585 euros with 10% monthly rate and a monthly payment of 500 euros for 4 months.

## Calculating the monthly payment

We have seen that over time the amount of interest decreases because the remaining capital also decreases (as shown on the figure). However, when you repay you loan, your monthly payments are the same throughout the loan period. Indeed, to help you manage your budget, the amount of interest is “smoothed” over the duration of the loan so that the amount of monthly payments is always the same during the whole period. For our example this amount is 500 euros.

The formula to compute the monthly payment or any periodic payment is:

Note: The monthly payment cannot be above certain percentage of your net income. For example in France, at most it’s going to be 33% of your net income.

# Know the total interest amount of your loan.

Once the amount of your monthly payment is known, it is quite easy to know the total amount of interest that will be payable over the entire loan period. To find it, just apply the following formula:

# Example with all formulas

Imagine that you got a loan of 100000€ with 2% annual interest rate for 20 years monthly payment. Now the first thing to do is compute the periodic rate:

Then, we need to compute the monthly payment.

Now we can know what is the total interest gain

# Conclusion

In this article we learned:

- What’s a credit/loan and what is an interest rate.
- What is a periodic interest rate and how to switch from annual interest rate to it and the math behind it.
- What are the components of your monthly payments and how in early months the paid capital is lower and the interest amount is higher.
- How to compute the monthly payments and what is the proof of its complicated formula.
- How to know the total interest amount you have in the whole period.
- And finally an example to summarize all things above.