Understanding how interest is calculated helps you compare loans, minimize what you pay, and make smarter borrowing decisions. Here are the key formulas with real worked examples.
Simple Interest vs. Amortizing Interest
Most personal loans, auto loans, and mortgages use amortizing interest — not simple interest. The distinction matters significantly.
| Type | How Interest Is Charged | Common For |
|---|---|---|
| Simple interest | Fixed percent of original principal each period | Short-term, some auto loans |
| Amortizing interest | Interest on remaining balance each period | Personal loans, mortgages, auto loans |
With amortizing loans, early payments are mostly interest and later payments are mostly principal — even though the payment stays the same each month.
Formula 1: Monthly Payment (Amortizing Loan)
$$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$
Where:
- M = monthly payment
- P = loan principal (amount borrowed)
- r = monthly interest rate (APR ÷ 12)
- n = total number of payments (years × 12)
Example: $15,000 personal loan at 10% APR, 48 months
- r = 10% ÷ 12 = 0.008333
- n = 48
- M = $15,000 × [0.008333 × (1.008333)^48] ÷ [(1.008333)^48 − 1]
- M = $380.44/month
Formula 2: Total Interest Paid
$$\text{Total Interest} = (M \times n) - P$$
Using the example above:
- Total paid = $380.44 × 48 = $18,261
- Total interest = $18,261 − $15,000 = $3,261
Loan Term Comparison — Same Rate, Different Terms
$20,000 personal loan at 10% APR:
| Term | Monthly Payment | Total Paid | Total Interest |
|---|---|---|---|
| 24 months | $922 | $22,128 | $2,128 |
| 36 months | $645 | $23,220 | $3,220 |
| 48 months | $507 | $24,336 | $4,336 |
| 60 months | $425 | $25,500 | $5,500 |
| 84 months | $332 | $27,888 | $7,888 |
Key insight: Choosing a 7-year term over a 3-year term saves $313/month but costs $5,760 more in total interest.
How Amortization Works Month by Month
For the first example ($15,000 at 10% APR, 48 months):
| Month | Payment | Interest Portion | Principal Portion | Balance |
|---|---|---|---|---|
| 1 | $380 | $125 | $255 | $14,745 |
| 12 | $380 | $115 | $265 | $13,670 |
| 24 | $380 | $95 | $285 | $11,200 |
| 36 | $380 | $68 | $312 | $8,000 |
| 48 | $380 | $3 | $377 | $0 |
Notice: Month 1 interest = $15,000 × (10% ÷ 12) = $125. As the balance falls, so does the interest charge — and more of each payment goes to principal.
APR vs. Interest Rate
Your interest rate determines the amortization calculation above.
Your APR includes the interest rate plus all mandatory fees, spread across the loan term.
Example: $10,000 personal loan, 12% stated rate, 2% origination fee ($200):
- Net proceeds: $9,800
- APR: ~14% (because you pay $200 in fees + $1,200/year in interest on $10,000 borrowed)
Always compare APRs when shopping loans — not just interest rates.
Making Extra Payments
Extra payments reduce principal faster, shortening the loan and cutting total interest:
$15,000 loan at 10% APR, 48 months — adding $50/month extra:
- Loan pays off in ~43 months (5 months early)
- Interest saved: approximately $300
Even small extra payments early in a loan (when the balance is highest) have an outsized effect on total interest.
Related: what is an installment loan · personal loans guide · pros and cons of debt consolidation · how to pay off debt in collections · credit card payoff calculator
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