What APR is and how it differs from the nominal rate
When a loan charges fees deducted at the time the credit is released — origination fees, required insurance, or processing charges — the amount that actually lands in the borrower's account is smaller than the full loan amount. Since the payment is still calculated on the full amount, but less money was actually received, the real cost of borrowing is higher than the nominal interest rate alone suggests. APR is that "real" rate, viewing the loan from the standpoint of how much money went out and how much came in over time.
Formulas used
Payment (from the nominal rate): P = L × i ÷ (1 − (1 + i)^−n)
Net amount received: Net = L − fees
APR (found by successive approximation): Net = P × (1 − (1 + APR)^−n) ÷ APR
Effective annual rate (APY): APY (%) = ((1 + periodic rate ÷ 100)^periods − 1) × 100
Where L is the loan amount, i is the nominal monthly interest rate, n is the number of payments, and P is the payment amount.
Practical example
A $10,000 loan at a 9% annual rate over 36 months, with $300 in fees deducted upfront, has a monthly payment of roughly $318, but the net amount received is only $9,700. That pushes the APR up to about 10.5% per year — more than a full percentage point above the 9% nominal rate stated in the contract, purely because of the fees.
Why two offers with the same nominal rate can cost very differently
It's common to see loan offers advertising the same interest rate but with very different fee structures. An offer with a lower nominal rate but high fees can end up costing more overall than one with a slightly higher nominal rate and low fees. APR solves this by putting both offers on the same unit of comparison: the real annualized cost, accounting for everything charged.
Why the effective annual rate tends to be higher than the nominal rate
When interest compounds more than once a year — say, a rate of 1.5% per month — simply multiplying that rate by 12 (giving 18% a year) ignores the interest-on-interest effect happening every month. The effective annual rate (also called APY) captures that compounding effect, so it's always a bit higher than the nominal rate whenever compounding happens more often than annually.
What this calculator doesn't account for
This simulation doesn't replace the official APR disclosed by a lender, which is regulated (Truth in Lending Act in the US) and must include all charges required by law. Treat the results as a comparison estimate between offers, and always check the official APR disclosure before signing any loan agreement.