Complete Guide to Loan Calculations
How does a loan work?
A loan is a financial agreement where an institution (bank, credit union, or lender) gives you a sum of money that you must repay in periodic installments, plus agreed interest. The most common system is the French amortization system, where you pay a fixed monthly payment that includes a portion of principal and interest.
At the beginning of the loan, most of your payment goes toward interest. As time progresses, this proportion reverses: you pay more principal and less interest. This happens because interest is calculated on the outstanding balance, which decreases with each payment.
The monthly payment formula (PMT)
Payment = P × [r(1+r)^n] / [(1+r)^n - 1]
Where:
- P = Principal (loan amount)
- r = Monthly interest rate (annual rate / 12 / 100)
- n = Total number of payments (years × 12 + additional months)
This formula ensures that by making all scheduled payments, the loan will be completely paid off.
Practical example
For a loan of $10,000 at 5% annual for 5 years (60 months):
- Monthly payment: $188.71
- Total to pay: $11,322.74
- Total interest: $1,322.74
This means that for borrowing $10,000, you'll end up paying an additional $1,322.74 in interest over the 5 years of the loan.
What is an amortization schedule?
An amortization schedule is a detailed breakdown of each of your payments. For each installment it shows:
- Payment number: The corresponding month
- Total payment: The fixed monthly installment
- Principal: How much of your payment reduces the debt
- Interest: How much you pay for using the money
- Balance: What you still owe
This table is essential for understanding how your debt evolves and planning possible early payments.
Factors that affect your loan
Interest rate
A 1% difference in rate can mean thousands of dollars on a large loan. For example, on a $200,000 mortgage over 30 years, going from 3% to 4% increases total interest by more than $40,000.
Loan term
- Short term: Higher payments, but less total interest
- Long term: More comfortable payments, but you pay more interest overall
Early payments
Making extra payments to principal can save you a lot of money in interest and reduce the loan term. Check that your loan doesn't have early payment penalties.
Frequently asked questions
The monthly payment is calculated using the PMT formula that considers the borrowed capital, interest rate, and number of payments. The formula guarantees that at the end of the term the loan will be fully paid, distributing principal and interest payments optimally.
It depends on your financial situation. A shorter term means higher payments but less total interest paid. A longer term reduces the monthly payment but significantly increases total interest. Evaluate your current and future payment capacity.
It's the most common system where the payment is constant throughout the loan. Each payment has a principal portion (which increases over time) and an interest portion (which decreases). At the start you pay more interest, at the end more principal.
Generally yes, as you reduce the outstanding principal and therefore future interest. First check if your loan has early payment fees. Many loans allow additional payments without penalty, which can save you significant money over the life of the loan.
The nominal interest rate is the pure interest on the loan. The APR (Annual Percentage Rate) includes the interest rate plus all associated costs (fees, required insurance, etc.). The APR gives you a more realistic view of the total loan cost.
Comparison: Short vs long term
Let's see how the term affects a $20,000 loan at 6% annual:
| Term | Monthly payment | Total paid | Interest | |------|-----------------|------------|----------| | 3 years | $608.44 | $21,904 | $1,904 | | 5 years | $386.66 | $23,200 | $3,200 | | 7 years | $292.86 | $24,600 | $4,600 | | 10 years | $222.04 | $26,645 | $6,645 |
As you can see, doubling the term from 5 to 10 years reduces the payment by almost half, but more than doubles the interest paid.
Related calculators
Complement your financial planning with these tools:
- Compound Interest Calculator - Calculate your investment and savings growth
- Percentage Calculator - Useful for calculating increases and discounts