The amortization formula, simple vs compound interest on personal loans, and why APR represents the true cost better than the interest rate.
A personal loan is a lump sum borrowed upfront and repaid in fixed monthly installments over a set term, typically 12 to 60 months. Each payment is split between interest and principal, and that split shifts over the life of the loan. Early payments are mostly interest, while later payments are mostly principal, a structure known as amortization.
According to the Federal Reserve, the average interest rate on a 24-month personal loan in the United States in 2025 was approximately 11.5 percent. Loan amounts commonly range from 1,000 to 50,000 dollars, and longer terms lower the monthly payment but increase total interest paid. A 10,000 dollar loan at 12 percent over 3 years costs about 332 dollars per month and 1,957 dollars in total interest; the same loan over 5 years drops the payment to 222 dollars but raises total interest to 3,347 dollars.
This tradeoff between payment size and total cost is the central decision in personal borrowing, and it is driven entirely by the amortization formula. Choosing a longer term feels cheaper month to month but can nearly double the interest paid over the life of the loan.
M = P × [ i(1 + i)^n ] / [ (1 + i)^n − 1 ]
| Variable | Meaning |
|---|---|
| M | Monthly payment |
| P | Principal (amount borrowed) |
| i | Monthly interest rate = annual rate ÷ 12 |
| n | Total number of payments (months) |
Worked example: borrow 15,000 dollars at 10 percent APR for 36 months. The monthly rate i = 0.10 ÷ 12 = 0.008333, and n = 36. Plugging into the formula gives M = 15,000 × [0.008333 × (1.008333)^36] / [(1.008333)^36 − 1] = 484.01 dollars per month. Over 36 months the total paid is 17,424 dollars, of which 2,424 dollars is interest.
The same formula governs mortgages and auto loans; only the rate, term, and principal change. The Consumer Financial Protection Bureau documents this calculation in its consumer loan resources. In the first month of the example loan, interest is 15,000 × 0.008333 = 125 dollars, so only 359 dollars of the 484 dollar payment reduces principal. By the final month, almost the entire payment is principal, which is the defining feature of amortization.
Simple interest is charged only on the original principal. The formula is I = P × r × t, where r is the annual rate and t is the time in years. A 5,000 dollar loan at 8 percent simple interest for 3 years costs 5,000 × 0.08 × 3 = 1,200 dollars in interest. Simple interest is common in short-term installment loans and some auto loans.
Simple interest = P × r × t
Compound interest is charged on principal plus accumulated interest. The formula is A = P × (1 + r/n)^(n×t), where n is the number of compounding periods per year. The same 5,000 dollars at 8 percent compounded monthly for 3 years grows to 5,000 × (1 + 0.08/12)^36 = 6,341 dollars, meaning 1,341 dollars in interest, about 12 percent more than simple interest over the same period.
Compound amount = P × (1 + r/n)^(n × t)
Most installment loans use amortization, which is a structured form of compound interest in which each payment resets the balance on which future interest is calculated. The key takeaway is that compounding frequency increases cost: daily compounding costs more than monthly, which costs more than annual, all at the same nominal rate. This is why the stated interest rate alone is not enough to compare loan products.
APR, or annual percentage rate, is the annualized cost of borrowing expressed as a single percentage. Unlike the nominal interest rate, APR includes certain fees such as origination fees, making it the most accurate single number for comparing loan offers. Under the Truth in Lending Act in the United States, lenders must disclose APR alongside the interest rate.
The difference between interest rate and APR can be significant. A 10,000 dollar loan with a 9 percent interest rate and a 3 percent origination fee (300 dollars) has an APR of roughly 11.5 percent over a 3-year term, because the fee is spread across the payments. Comparing only the interest rates would make the loan look cheaper than it actually is, which is exactly why APR exists as a standardized comparison metric.
To find total cost, multiply the monthly payment by the number of payments and subtract the principal. For the 15,000 dollar example: 484.01 × 36 = 17,424 dollars total paid, minus 15,000 principal equals 2,424 dollars in interest. The Metriova loan calculator runs this full amortization and displays both the payment schedule and the total interest, so the real cost of any term or rate is visible before you borrow.
Loan Calculator — Fixed vs Variable Rate Comparison
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