Calculation of Interest and Amortization Schedule for a Mortgage Loan
A mortgage loan allows an individual with stable financial income to purchase real estate even if they do not yet have sufficient liquidity for such a purchase. The borrower is responsible for repaying the amount lent by the financial institution. This repayment amount is increased by interest, which is formally detailed within the loan contract.
Additionally, an insurance premium is typically added to this amount, as the lending institution seeks to protect itself against the potential insolvency of the borrower during the term of the contract.
Formulas for Calculating Interest and Monthly Payments
The borrower must repay a monthly installment at each due date, with the total number of installments being calculated by multiplying the loan term in years by 12 (as there are 12 monthly payments per year).
This monthly payment amount does not yet include insurance. It consists of repaying the principal amount borrowed (C0), as well as the sum of the interest (i) applied to each installment. The nominal interest rate (t) is typically an annual rate that is proportionally applied across all monthly payments rather than being applied once to the total loan amount.
The formula to calculate the monthly payment (M) is as follows:
M = [C0 × t / 12] / [1 − (1 + t / 12) ^ (-n)]
where:
- C0 is the principal amount (initial loan),
- t is the annual nominal interest rate,
- n is the total number of payments (number of years of the loan multiplied by 12).
The total interest paid over the life of the loan is then calculated as the sum of all the monthly payments minus the principal amount borrowed:
Total Interest = n × M - C0
Numerical Application
When the fixed interest rate (t) is 1.2%, for a loan amount of €180,000 over 25 years, applying the formula will give:
M = [180,000 × 1.2 / 12] / [1 − (1 + 0.012 / 12) ^ (-300)] ≈ €694.79
The total interest paid over the life of the loan will then be:
(300 × 694.79) - 180,000 = €28,437.29
Additional Costs
The payments related to the annual insurance rate (ta) are calculated differently. Typically, the total annual insurance costs are spread evenly over the twelve monthly installments, and then multiplied by the number of years of the mortgage. The formula to obtain the total insurance amount is as follows:
[(C0 × ta) / 12] × Number of years
Where:
- C0 is the principal amount (initial loan),
- ta is the annual insurance rate.
Les frais annexes
Les versements liés au taux annuel d’assurance ta se calculent différemment. Il s’agit le plus souvent de lisser le montant total des frais d’assurance annuels sur les douze mensualités puis de multiplier par le nombre d’années du prêt immobilier. Ainsi, la formule pour obtenir le montant total de l’assurance est la suivante: [(C0 x ta) / 12] x Nombre d’années.