Calculating Mortgage Interest

Calculating interest is often a source of confusion for beginners when taking out their first mortgage.

It would seem logical to think that borrowing €150,000 at a 4% rate means paying 4% of €150,000, which is €6,000.

However, this is unfortunately incorrect, and borrowing money is actually much more expensive than that.

Explanation

Interest rates are calculated monthly on the remaining capital owed to the bank.

Let’s imagine someone takes out a loan with the following details:

• Borrowed amount: €150,000
• Interest rate: 4%
• Insurance rate: 0.36%
• Term: 20 years

Calculating Monthly Payments

First, we need to know the monthly payments that the person will repay with the given configuration:

To calculate your monthly payment amount (m), you need to know several elements:

• the borrowed capital (C),
• the interest rate (r)
• the number of years (n).

The formula is as follows:

C = 150,000
r = 0.04
n = 20
///
M = (C x r/12) / (1 – (1 + r/12)-12 x n)
///
908 ~= (150000 x 0.04/12) / (1 – (1 + 0.04/12)-12 x 20)

This gives us a monthly payment of €908, not including insurance.

We then add the insurance of €45 per month because:

• (Borrowed capital x Insurance rate) / 12
• => (150000 x 0.0036) / 12 = 45

Which equals: €953 monthly payment as 908€ + 45 = 953

Calculating Interest and Loan Cost

We now know that the person will need to pay €953 per month to repay their loan.

Let’s see how this repayment is structured and especially why taking out a loan is more expensive than simply the interest rate applied to the borrowed capital.

To do this, let’s break down the monthly payment to calculate how much interest we’ll repay in the total monthly payment. You need to understand the following calculation:

(Remaining capital to repay x Interest rate) / 12

Thus, following this calculation, the first monthly payment of our loan breaks down as follows:

• (150000 * 0.04) / 12 = 500 + 45 (insurance/month) = 545
• 953 - 545 = 408

To summarize: after your first payment of €953 to repay your first loan installment, you have:

• Paid €545 in loan interest, representing the cost of the loan, as money isn’t free.
• And increased your equity by €408, because from the initial borrowed capital of €150,000, you’ve repaid €408 for yourself.

Then, the calculation for the next installment evolves.

We no longer start from the initial €150,000 capital to repay, but from these initial €150,000 minus the capital already repaid, that is, the €408 already repaid during the previous installment. So the calculation would look like this:

• ((150000 - 408) * 0.04) / 12 = 498.64 + 45 (insurance/month) = 543.64
• 953 - 543.64 = 409.36

Do you see the principle? And this operation is repeated for the number of installments agreed with the bank, in our case, 240 times for 20 years, or 240 months.

We can also observe that over time:

• We have less interest to repay.
• And more capital to repay.

This means that at the beginning of a loan, we’re mainly repaying the cost of the money borrowed from the bank, but over time, we’re setting aside more money that directly increases our net worth.

It’s also interesting to note that the borrowed capital on which we make the calculation has been fully released. Indeed, when buying a property with renovation work, for example, the total capital is released as the work is completed, so the monthly payment evolves according to the capital released until all the borrowed capital is fully released. This same case can also apply to off-plan properties, where funds are gradually released as the apartment is built.

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