The short answer
A $10,000 loan paid off at $300/month over 36 months carries a 5.06% APR and $800 in total interest. That same 5% rate, if compounded monthly instead of stated as a flat APR, becomes a 5.1162% APY. And a 6% loan with $3,000 in fees rolled in effectively costs 6.29% — the fees are the difference between the sticker rate and what you actually pay.
Key takeaways
- $10,000 at $300/month for 36 months implies a 5.06% APR — a way to check whether a quoted rate matches the payment you're actually being asked for.
- A 5% APR compounded monthly is a 5.1162% APY — APY is always the higher number whenever compounding happens more than once a year.
- $3,000 in fees on a $100,000, 6% loan pushes the effective rate to 6.29% — the fees make the loan cost more than the sticker rate says, even though the sticker rate never changes.
- On a $200,000, 30-year loan, 5% versus 9% is $1,073.64 versus $1,609.25 a month — and $192,816.71 more in total interest over the loan's life.
Finding the rate behind a known payment
Sometimes you know the loan amount, the monthly payment, and the term — but not the rate itself. That happens with older loans, informal financing, or offers presented only as a monthly figure. Working backward from a $10,000 loan at $300/month for 36 months:
Implied APR: 5.06%
Total payments: $10,800.00 ($300 × 36)
Total interest: $800.00
There's no closed-form formula to solve for rate directly — the calculator iterates toward the rate that makes the standard loan payment formula match the payment you entered, which is exactly what happens behind the scenes on financial calculators and spreadsheets alike.
APR vs APY: why compounding changes the number
APY = (1 + APR ÷ n)^n − 1
= (1 + 0.05 ÷ 12)^12 − 1 = 5.1162%
APR is the simple, stated annual rate; APY accounts for interest compounding within the year. A 5% APR compounded monthly actually yields 5.1162% over a full year — a 0.1162 percentage point gap that widens as compounding gets more frequent (daily compounding pushes it slightly higher still than monthly).
How fees turn a nominal rate into an effective rate
A quoted rate assumes you receive the full loan amount. In practice, origination fees and points are subtracted upfront, so you're repaying a larger amount than you actually received. On a $100,000 loan at 6% nominal with $2,000 origination plus 1 point ($1,000):
Total fees: $2,000 + $1,000 = $3,000
Net proceeds actually received: $97,000
Effective annual rate: 6.29% (versus 6.00% nominal)
Without any fees, the effective rate and nominal rate are identical — this calculator's own zero-fee case confirms that a $100,000, 6% loan with no origination costs computes to exactly 6.00% effective. Fees are what create the gap, which is why comparing loans on effective rate rather than the advertised nominal rate matters most when offers include different fee structures.
Related calculators
- APR Calculator — compute a loan's APR directly from the loan amount, rate, term, and fees.
- Loan Calculator — run a full payment schedule once you know the rate you want to compare.
- Mortgage Calculator — apply rate comparisons to a specific home loan scenario.