📊 APR Calculator
The advertised rate prices the money. The APR adds the fees, which is why two loans at the same rate can cost very different amounts. This finds the real annual rate once everything is counted.
Why the APR is higher than the interest rate, and what it is hiding
The interest rate tells you what the lender charges on the balance. The APR tells you what the loan costs once the fees are folded in and spread across the term. They are different numbers for the same loan, and the gap between them is the clearest signal of how much of the price has been moved out of the rate and into the fees.
APR solves: Amount received − Fees = Σ Paymentt / (1 + APR/12)t
There is no closed-form solution. The APR is found by iteration: the rate at which the payments you will make, discounted back to today, equal the money you actually received. That is why every APR is computed numerically, including by this calculator.
The same rate, different APRs
| Fees and points | Monthly payment | APR | Gap |
|---|---|---|---|
| $0 | $1,798.65 | 6.000% | — |
| $2,000 | $1,798.65 | 6.062% | +0.062 |
| $4,000 | $1,798.65 | 6.126% | +0.126 |
| 1 point + $4,000 | $1,798.65 | 6.222% | +0.222 |
| $9,000 | $1,798.65 | 6.287% | +0.287 |
The monthly payment is identical in every row, because fees do not change the repayment schedule — they change what you received for it. This is exactly why comparing monthly payments across lenders tells you nothing about which loan is cheaper, and why the APR exists as a disclosure requirement.
The APR's blind spot: it assumes you go the distance
An APR spreads the fees across the full term. Pay a loan off early and the fees are spread across fewer years, so the effective cost rises sharply. A $4,000 fee on a thirty-year $300,000 mortgage adds 0.126 points to the APR; the same fee on a loan you refinance or sell out of after four years costs far more per year than the APR suggests.
| Years held | Effective annual cost | Versus quoted APR |
|---|---|---|
| 30 years | 6.126% | As quoted |
| 10 years | 6.192% | +0.07 |
| 7 years | 6.246% | +0.12 |
| 4 years | 6.388% | +0.26 |
| 2 years | 6.723% | +0.60 |
The practical rule follows directly: pay points and fees to buy down the rate when you are confident you will hold the loan a long time, and refuse them when you might move, refinance or overpay. The refinance calculator works out the break-even month explicitly.
A lender who cannot beat a rival on rate can still win on monthly payment by extending the term, and win on headline rate by loading the fees. The APR catches the second trick and not the first. Compare APR and term together, or you have only closed one of the two gaps.
APR, APY and the nominal rate
These three get used interchangeably and mean different things. The nominal rate is the quoted annual rate before compounding and before fees. The APY — or AER on a savings account — adds the effect of compounding within the year. The APR adds the fees but, in the US convention, not the intra-year compounding. So on a loan with no fees, the APR equals the nominal rate even though the amount you actually pay reflects monthly compounding.
The consequence is that a US APR slightly understates the true annual cost of a monthly-compounded loan, while a UK or EU APR, which does include compounding, will read marginally higher for the same loan. The interest rate calculator converts between the three conventions.
What lenders may leave out
Not every cost is required to be in the APR, and the exclusions vary by jurisdiction and loan type. On a US mortgage the APR typically includes origination fees, points, mortgage insurance and some closing costs, but excludes the appraisal, title insurance, credit report and recording fees. That means two lenders quoting identical APRs can still have a four-figure difference in cash due at closing.
The defence is to ask for the total of all costs in cash, not just the APR, and compare that alongside it. Two numbers — APR and cash to close — catch almost everything a single number misses.
A worked example
Two offers on $250,000 over 30 years. Lender A quotes 6.25% with no fees: the payment is $1,539.29 and the APR is 6.250%. Lender B quotes 5.875% with one point and $3,200 of fees: the payment is $1,478.84 and the APR is 6.090%. B is cheaper on both payment and APR, so if you keep the loan it wins. But B costs $5,700 up front, and the payment saving is $60.45 a month — so the break-even is at 94 months, just under eight years. Moving within eight years makes the higher-rate loan the cheaper one.
Two neighbours worth knowing: the interest rate calculator, for the question this one leads into, and the loan calculator, which answers it from the other direction.
Frequently Asked Questions (FAQs)
What is the difference between APR and interest rate?
The interest rate is what you pay on the balance. The APR adds the fees and points and expresses the whole cost as one annual rate, so it is the better basis for comparing loans of the same term. A loan with no fees has an APR equal to its interest rate.
Why is my APR higher than the rate I was quoted?
Because the APR includes origination fees, points and certain closing costs spread over the term. A gap of 0.1 to 0.3 points on a mortgage is normal. A much larger gap means the fees are substantial relative to the loan, which is worth questioning.
Is a lower APR always the better loan?
Only if the terms are the same length and you keep the loan to term. The APR spreads fees over the full term, so a low-APR loan bought with large up-front fees becomes the expensive option if you repay early, refinance or move. Compare the APR, the term, and the cash due up front together.
Does the APR include everything I pay?
No. Which costs must be included varies by country and loan type. US mortgage APRs typically exclude appraisal, title insurance, credit report and recording fees, so ask for the total cash cost as well as the APR.
What is the difference between APR and APY?
APY includes the effect of compounding within the year; APR, in the US convention, includes fees but not intra-year compounding. On savings you want the highest APY; on borrowing you want the lowest APR, and on a monthly-compounded loan the true annual cost is slightly above the stated APR.
Are points worth paying?
They are a bet on how long you will hold the loan. Each point typically costs 1% of the loan and cuts the rate by roughly 0.25 points, which pays back over about five to eight years. Hold the loan longer and you win; move, refinance or overpay sooner and you lose.
Can an APR be lower than the interest rate?
Rarely, but yes, when a lender credit or rebate offsets the fees, or when the loan carries a subsidy. A negative fee reduces the effective cost below the nominal rate, which the APR correctly reflects.