Understanding Loan Interest Calculation
Loan interest calculation is based on a precise mathematical formula that takes into account
three essential elements: the borrowed amount (principal), the annual interest rate, and the repayment duration.
This calculation method ensures constant monthly payments throughout the loan term.
Monthly Payment Calculation Formula
The formula used to calculate monthly payments for a compound interest loan is:
M = P × [r × (1 + r)ⁿ] / [(1 + r)ⁿ - 1]
- M = Monthly payment
- P = Principal (borrowed amount)
- r = Monthly interest rate (annual rate ÷ 12)
- n = Total number of monthly payments
Compound Interest Principle
In a standard loan, interest is calculated on the remaining principal. This means that:
- Early in the loan: the interest portion of each payment is significant because the remaining principal is high
- Late in the loan: the interest portion decreases as the remaining principal diminishes
- Monthly payment stays the same but the principal/interest distribution evolves
Practical Calculation Example
Mortgage Loan of $200,000
- Amount: $200,000
- Rate: 3.5% per year
- Term: 20 years (240 months)
Monthly rate calculation:
r = 3.5% ÷ 12 = 0.292% = 0.00292
Formula application:
M = 200,000 × [0.00292 × (1.00292)²⁴⁰] / [(1.00292)²⁴⁰ - 1]
Monthly payment ≈ $1,160
Total cost:
- Total repaid: $1,160 × 240 = $278,400
- Total interest: $278,400 - $200,000 = $78,400
Factors Affecting Loan Cost
Interest Rate Impact
A variation in interest rate has a considerable impact on the total loan cost:
Annual Rate |
Monthly Payment ($200k, 20 years) |
Total Interest Cost |
2.5% |
$1,060 |
$54,400 |
3.5% |
$1,160 |
$78,400 |
4.5% |
$1,266 |
$103,840 |
Loan Term Impact
Extending the term reduces monthly payments but increases total cost:
Term |
Monthly Payment ($200k, 3.5%) |
Total Interest Cost |
15 years |
$1,430 |
$57,400 |
20 years |
$1,160 |
$78,400 |
25 years |
$1,001 |
$100,300 |
Types of Loans
Fixed-Rate Loan
The rate remains the same throughout the loan term. Monthly payments are constant and predictable.
Advantage: security and predictability. Disadvantage: no benefit if rates drop.
Variable-Rate Loan
The rate varies according to a reference index. Monthly payments can fluctuate.
Advantage: initial rate often lower. Disadvantage: uncertainty about evolution.
Tips to Optimize Your Loan
- Negotiate the rate: Even 0.1% difference represents thousands of dollars over the total term
- Down payment: The larger the down payment, the less you borrow and pay in interest
- Optimal term: Find the right balance between affordable payment and total cost
- Early repayment: Option to reduce term or monthly payments
- Loan insurance: Include in total cost calculation
Simulate Before Committing
Our calculator allows you to compare different scenarios and make an informed decision.
Don't hesitate to test several combinations of amount, rate, and term to find the solution that best
fits your financial situation.
Remember: A loan is a long-term commitment. Take time to understand the financial mechanisms
and don't hesitate to consult a banking advisor for personalized advice.