Three formulas cover nearly every loan: simple interest (I = P × r × t) for short-term loans, the amortized payment formula for mortgages and car loans, and total interest = (monthly payment × number of payments) − principal. Example: a $20,000 car loan at 7% for 5 years costs $396.02/month — $3,761.44 in total interest.
Formula 1: simple interest
I = P × r × t — principal × rate × time.
Borrow $5,000 at 8% for 2 years: $5,000 × 0.08 × 2 = $800 in interest. You'll repay $5,800 total.
Simple interest shows up in short-term personal loans, some auto loans, and private lending. It's the honest formula — what you see is what you pay.
Formula 2: the amortized payment (mortgages, car loans)
Most big loans amortize — each payment covers that month's interest plus a slice of principal. The monthly payment is:
M = P × [r(1+r)^n] / [(1+r)^n − 1], where r is the monthly rate and n is the number of payments.
$20,000 car loan at 7% for 60 months: r = 0.07/12, n = 60 → $396.02/month.
| Early payments | Late payments | |
|---|---|---|
| Goes to interest | Most of it | Very little |
| Goes to principal | Very little | Most of it |
That's why extra payments early in a loan are so powerful — they attack principal when the interest portion is fattest.
Tip: One extra payment per year on a 30-year mortgage can shave roughly 4 years off the loan. The math rewards early aggression.
Formula 3: total interest (the number that matters)
Total interest = (monthly payment × number of payments) − principal.
Our car loan: ($396.02 × 60) − $20,000 = $3,761.44. That's the true price of borrowing — always compute it before signing.
Two loans with the same rate can have wildly different total interest if the terms differ. A 7-year car loan at 7% costs about $1,400 more in interest than the 5-year version, even though the rate is identical.
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How do I calculate interest on a loan manually?
For simple loans: principal × rate × time. For amortized loans (mortgage, auto): use M = P[r(1+r)^n]/[(1+r)^n−1] with the monthly rate. Or skip the algebra and use a calculator.
Why is my first mortgage payment almost all interest?
Amortization front-loads interest because interest is charged on the full outstanding balance, which is biggest at the start. As principal shrinks, the interest slice shrinks with it.
Does paying extra principal really help?
Yes — every extra dollar goes straight to principal, which reduces all future interest charges. Extra payments early in the loan save the most.
General information only, not financial advice.