# How do you calculate mortgage repayments? Introducing the method and simulation examples – jobmode

**Calculating mortgage repayments** involves **determining the monthly amount** you need to pay in order to repay the loan over its term.

**“mortgage” **This is typically done using the formula for the monthly payment on an amortizing loan. The formula is:

$M=(+r)n−P⋅r⋅(+r)n$

Where:

- $M$ = Monthly Payment
- $P$ = Principal Loan Amount (the initial amount borrowed)
- $r$ = Monthly Interest Rate (annual interest rate divided by 12 months and converted to decimal)
- $n$ = Total Number of Payments (loan term in months)

Let’s illustrate this with an example:

**Example**: Suppose you take out a 30-year mortgage for $250,000 at an annual interest rate of 4%. First, convert the annual interest rate to a monthly rate:

$r=120.04 =0.003333$

Next, calculate the total number of payments:

$n=30×12=360$

Now, plug these values into the formula:

$M=(+)360−,⋅⋅(+)360 $

Using this formula, you’ll find that the monthly payment for this mortgage is approximately $1,194.93.

**Simulation Example**:

Let’s simulate the first few months of repayments for this mortgage:

## Month 1:

- Interest Payment = 250,000 \cdot 0.003333 = $833.33
- Principal Payment = $1,194.93 – $833.33 = $361.60
- Remaining Loan Balance = $250,000 – $361.60 = $249,638.40

## Month 2:

- Interest Payment = 249,638.40 \cdot 0.003333 = $832.13
- Principal Payment = $1,194.93 – $832.13 = $362.80
- Remaining Loan Balance = $249,638.40 – $362.80 = $249,275.60

### Month 3:

- Interest Payment = 249,275.60 \cdot 0.003333 = $830.92
- Principal Payment = $1,194.93 – $830.92 = $364.01
- Remaining Loan Balance = $249,275.60 – $364.01 = $248,911.59

And so on, for the duration of the loan term.

This simulation demonstrates how the monthly payments are divided between interest and principal, and how the remaining balance gradually decreases over time.

Keep in mind that this is a simplified example, and in reality, factors like taxes, insurance, and potential changes in interest rates or loan terms may affect your actual mortgage payments. Always consult with a financial advisor or use specialized mortgage calculators for precise calculations.

### When taking out a mortgage, you need to simulate two types of money.

One is the monthly repayment amount. If you don’t check whether you can afford to repay the loan each month, you may end up late in repayments and incur late payment interest.

The other is the total cost (total payment amount). When purchasing a home, there are various costs such as stamp duty and registration fees, in addition to the price of the home itself. By simulating how much the total cost (total payment amount) will be, it becomes clear how much it will cost in total to purchase a home.

This article explains how to simulate a mortgage loan. Please use this as a reference to assemble a mortgage that suits you.

**About mortgage repayment amount**

There are two types of home loan repayments: the monthly repayment amount and the total cost (total payment amount), and you need to understand the difference between them.

The first is the monthly repayment amount. If your monthly repayments are too high, your household finances will be strained and your repayments may be delayed. If you continue to be in arrears, you may lose your right to the house, so set your monthly repayment amount to an amount that you can afford.

The second is the total cost (total payment amount). The total cost (total payment amount) is the total amount of payments that will occur due to taking out a home loan.

For example, if you borrow 30 million yen as a home loan, the amount you have to repay to the financial institution is not 30 million yen.

Interest depending on the interest rate and borrowing period, borrowing fees, guarantee fees, and registration and license tax are also required for registration of mortgages. Additionally, if you request a judicial scrivener to handle the mortgage registration process, you will also be required to pay the judicial scrivener’s fees, so the total amount of these costs is called the total cost (total payment amount).

How to calculate monthly mortgage repayment amount

The monthly mortgage repayment amount is calculated using the following formula.

Monthly repayment amount = Monthly interest x (1 + monthly interest) ＾ Total number of repayments ÷ {(1 + monthly interest) ＾ Total number of repayments – 1} x Borrowed amount

*^ indicates a power.

*Calculation formula for equal repayment of principal and interest. The calculation formula is different for equal principal repayments.

This is difficult to calculate using a regular calculator, so a special tool such as a financial calculator is required.

If the calculation is difficult, please use the simulation tool available on the financial institution’s website.

With our simulation tool, you can instantly calculate your monthly repayment amount. Use it to find out how to set the loan amount and repayment period so that you can easily repay the loan.

au Jibun Bank Mortgage Loan Simulation

Monthly interest calculation

Monthly interest rate is the interest rate per month. Mortgage interest rates are usually expressed as an annual rate, so divide by 12 to get the monthly rate.

For example, if the applicable interest rate is 1.2% per year, the monthly interest rate is 1.2 ÷ 12 = 0.1%. % is converted into a number by multiplying it by 0.01, so substitute 0.1% x 0.01 = 0.001 into the monthly interest portion of the above formula.

Calculating the number of repayments

Repayment frequency is the number of times repayments occur. If you repay once a month, the number of repayment months = the number of repayments.

For example, for a 35-year mortgage, the number of repayments is 35 x 12 months = 420 months, so the number of repayments is 420.

Simulate by applying the calculation formula

Now, let’s actually apply the formula to find the monthly repayment amount.

For example, if the loan amount is 30 million yen, the interest rate is fixed for 35 years, the applicable interest rate is 1.2% per annum, and the principal and interest are equal repayments, the number of repayments will be 35 x 12 = 420 times, and the monthly interest rate will be 0.001, so the following is as follows: Calculate using the formula.

Monthly repayment amount = Monthly interest x (1 + monthly interest) ＾ Total number of repayments ÷ {(1 + monthly interest) ＾ Total number of repayments – 1} x Borrowed amount

0.001×(1+0.001)＾420÷{(1+0.001)＾420-1}×30,000,000 yen

The monthly repayment amount will be approximately 87,510 yen.

How to calculate the total cost of a mortgage loan (total payment amount)

Once you have determined your monthly repayment amount, you can also calculate the approximate total cost (total payment amount) using the formula below.

Total cost (total payment amount) = monthly repayment amount x number of repayments + miscellaneous expenses

*No bonus payment. If the interest rate does not change during the repayment period.

If miscellaneous expenses cost 1 million yen, the total cost (total payment amount) can be calculated as approximately 37.75 million yen using the formula below.

Total cost (total payment amount) = monthly repayment amount x number of repayments + miscellaneous expenses

Approximately 87,510 yen x 420 times + 1 million yen = approximately 37,754,200 yen

Easily calculate your mortgage repayment amount using a simulation tool

As mentioned earlier, calculating the mortgage repayment amount is not easy.

If you want to find out the monthly repayment amount and total cost (total payment amount) of your mortgage, please use the simulation tools available on each financial institution’s website. Depending on the financial institution, you can also simulate the amount you can borrow.

Using simulation tools, you can plan a mortgage that is right for you. For example, you can change the monthly repayment amount in 10,000 yen increments to find out how much the borrowing amount changes, or you can shorten or extend the repayment period to calculate the monthly repayment amount that is easier to repay.

Substitute various numbers into the simulation tool to create the best repayment plan for you.

Understand the characteristics of each simulator

Generally, each simulation tool has settings such as interest rate type (fixed interest rate, variable interest rate, etc.) and repayment method (equal principal and interest repayment method, equal principal repayment method) that are applied by the financial institution. It’s a target.

If you have already decided on the financial institution you would like to use, please use the simulation tool provided.

For example, au Jibun Bank releases the following three simulation tools for new home loan users.

### Find out your monthly repayment amount

Find out how much you can borrow based on your current annual income

Find out how much you can borrow based on your monthly repayment amount

With au Jibun Bank’s simulation tool, you can specify the repayment method, so you can simulate not only when borrowing with the equal principal and interest repayment method, but also when borrowing with the equal principal repayment method.