The true cost of borrowing: APR, fees, flat rates and early repayment
The rate a lender quotes is rarely the whole price of a loan. Fees are taken from the money you receive, some loans charge interest on the original amount for the whole term, and a loan repaid early costs more per year than the same loan held to the end. This lesson works out the true yearly cost of a loan with a live calculator, compares two offers where the lower rate is not the cheaper loan, and shows why a flat rate is not what it appears to be.
- Level
- Beginner
- Reading time
- About 24 minutes
- Know this first
- How banks work
By the end you will be able to:
- explain why the quoted interest rate and the true cost of a loan differ
- calculate a loan's APR from the payments and the cash actually received
- show how a fixed fee raises the yearly cost of a short loan or an early repayment
- convert a flat-rate quote into a true yearly rate
- compare two loan offers by total cost and APR, not by the headline rate
The rate on the advert is not the price
Two loans can show the same rate and cost very different amounts. A lender may take a fee out of the money it hands over, so the borrower pays interest on more than was received. It may calculate interest on the full original amount for the whole term, long after most of that amount has been repaid. Or the borrower may repay early, and the fee, which is paid once at the start, is then spread over a shorter time. In each case the true yearly cost is higher than the quoted rate.
The lesson on annuities and loans showed how a level payment is worked out, and the lesson on compound interest showed how the way interest is added changes the effective rate. This lesson builds on both to answer a practical question: what does a loan really cost? It uses a fictional $20,000 loan so that every figure can be checked, and no company's accounts are used.
APR: the rate with the fees counted
The interest rate is, in the words of the US Consumer Financial Protection Bureau, the cost paid to the lender for borrowing money, and it does not reflect fees or other charges. The annual percentage rate, or APR, is a broader measure: it combines the interest rate with certain charges made to get the loan, such as origination fees and points. That is why the bureau advises comparing APRs with APRs and not APRs with interest rates. Many countries have a similar disclosure rule, but the exact definition of the APR and of the fees included differs from place to place, so check the one that applies to you.
The idea behind the number is simple. The borrower receives less than the loan amount, because the fee is taken off, and then makes the full payments. The APR is the yearly rate at which those payments are worth exactly the cash the borrower received. It is found by trial, since no formula solves it directly, and a spreadsheet or calculator does that in a second.
With no fee and a loan held to the end, j is the quoted monthly rate and the APR equals the quoted rate. Everything above that is the cost of the fee. The effective annual rate is higher than the APR because it counts the compounding of the monthly rate over the year.
Price the loan
The loan is $20,000, repaid in equal monthly payments. Set the quoted rate, the length of the loan, the fee that is taken off the amount paid out, and when the loan is repaid. The left page shows the loan as quoted; the right page shows what a flat-rate loan quoted at the same rate would be, as explained further down.
A $20,000 loan at 8.00% over 3 years has a payment of $627 a month. The 2.0% fee takes $400 off the amount paid out, so the borrower receives $19,600. Held to the end, the loan costs $2,962 in interest and fees, a true yearly rate of 9.38% against the quoted 8.00%. A flat-rate loan quoted at the same 8.00% would cost $2,238 more in interest and is really a rate of 14.55%.
Four experiments. First, at the starting settings the loan has a payment of $627 a month and a fee of $400, so the borrower receives $19,600 and pays $2,962 in interest and fees. The quoted rate is 8.00%, but the true yearly rate is 9.38% and the effective annual rate 9.79%. Second, set the fee to none: interest and fees fall to $2,562 and the true rate falls back to exactly 8.00%. The whole difference in rate is the fee. Third, put the fee back and move the repayment to 50% of the term, which is 18 months. The fee is the same $400, now earned over half the time, and the true rate rises to 9.83% while interest and fees fall to $2,278. Fourth, shorten the loan to one year with the fee and the full term: the true rate climbs to 11.82%, because the same fee is spread over a single year. A fee is a fixed price paid at the start, so the shorter the time the loan is held, the more it costs per year.
How fees and timing combine
The grid shows the true yearly rate on an 8.00% three-year loan for different fees and different times of repayment. The quoted rate never changes, and the true rate does.
| True yearly rate (APR) on a quoted 8.00%, 3-year loan | Settled after 9 months | Settled after 18 months | Held for the full 36 months |
|---|---|---|---|
| No fee | 8.00% | 8.00% | 8.00% |
| Fee of 1% | 9.54% | 8.91% | 8.68% |
| Fee of 2% | 11.10% | 9.83% | 9.38% |
| Fee of 3% | 12.67% | 10.76% | 10.08% |
| Fee of 5% | 15.89% | 12.65% | 11.52% |
The first row confirms the rule: with no fee, the true rate is 8.00% whenever the loan is repaid, because interest is charged only for the time the money is out. Each row below it rises as the repayment comes earlier, and each column rises with the fee. A lender can therefore offer a low quoted rate and make up the difference in the fee, and the borrower who expects to repay early is the one who pays most for it.
Comparing two offers
Suppose a borrower is choosing between two offers for the same $20,000 over three years. Offer A quotes 7.50% with no fee. Offer B quotes a lower 6.50% but takes a 3% fee. Offer B has the lower rate and the lower monthly payment, so it looks like the better deal.
| $20,000 loan over 3 years | Offer A | Offer B |
|---|---|---|
| Quoted yearly rate | 7.50% | 6.50% |
| Fee taken from the amount paid out | None | $600 (3%) |
| Cash received | $20,000 | $19,400 |
| Monthly payment | $622 | $613 |
| Interest and fees if held to the end | $2,396 | $2,667 |
| True yearly rate (APR) if held to the end | 7.50% | 8.56% |
| Interest and fees if settled after 18 months | $1,758 | $2,119 |
| True yearly rate (APR) if settled after 18 months | 7.50% | 9.24% |
Offer B's payment is $613 against $622, but over three years it costs $2,667 in interest and fees against $2,396 for Offer A. Counting the fee, its true yearly rate is 8.56% against 7.50%. If the borrower repays after 18 months, the gap widens in percentage terms: Offer B's true rate rises, and Offer A's stays at its quoted rate because it has no fee. The lower payment is real, but it is bought with money taken at the start. Compare total cost and APR, and then check how long you expect to keep the loan.
Flat rates: interest on money already repaid
Some lenders in some markets quote a flat rate. Interest is worked out on the original amount for the whole term, added to the loan, and the total is divided into equal payments. Because the balance falls with every payment, the borrower has the use of much less than the original amount for most of the term, but pays interest as if the full amount were owed throughout. A reducing-balance loan, the usual kind in the earlier lessons, charges interest only on what is still owed.
| $20,000 over 3 years | Flat-rate payment | Flat-rate interest | True yearly rate | Reducing-balance payment, same quoted rate | Reducing-balance interest |
|---|---|---|---|---|---|
| Flat rate of 4% | $622 | $2,400 | 7.51% | $590 | $1,257 |
| Flat rate of 6% | $656 | $3,600 | 11.08% | $608 | $1,904 |
| Flat rate of 8% | $689 | $4,800 | 14.55% | $627 | $2,562 |
| Flat rate of 10% | $722 | $6,000 | 17.92% | $645 | $3,232 |
At the starting settings the flat-rate loan quoted at 8% charges $4,800 of interest, for a payment of $689 a month, and the true yearly rate is 14.55%, close to double the quote. This is the usual pattern: the true rate on a flat-rate loan is a little under twice the flat rate, as the table shows. A flat 5% is far from a 5% loan. When a lender gives a flat rate, ask for the APR.
What the APR cannot tell you
- It assumes the rate stays fixed. For an adjustable-rate loan the APR does not reflect how high the rate could rise, so adjustable and fixed APRs should not be compared directly.
- It depends on the loan type and the rules. A closed-end loan's APR includes fees, and a revolving credit line's APR may not, so the two are not directly comparable. Countries also differ in which charges are counted.
- It cannot know when you will repay. The standard APR assumes the loan runs to the end. The calculator shows how far the true cost moves when it does not.
- It leaves out some costs. Late fees, optional insurance and penalties for repaying early may sit outside it.
- It does not say whether the loan is a good idea. A cheap loan for something you cannot afford is still a bad loan.
Common mistakes
Comparing the quoted rate of one loan with the APR of another
Compare like with like. The quoted rate leaves out the fee and the APR includes it.
Choosing the loan with the lowest monthly payment
A lower payment can come from a longer term or from a fee taken at the start, and either can raise the total cost.
Ignoring the time you expect to hold the loan
A fee is a fixed cost. If you may repay early, a loan with a fee is more expensive than its APR suggests.
Taking a flat rate for a true rate
A flat rate charges interest on the original amount throughout. The true yearly rate is close to double.
Forgetting that the borrower receives less than the loan
When the fee is taken from the proceeds, interest is paid on the full amount although only part was received.
Try it yourself
1. A lender gives $1,000 for one year, charges a $20 fee out of the amount paid out, and the borrower repays $1,080 at the end of the year. What is the true yearly rate?
Show the working
The borrower receives 1,000 − 20 = $980 and repays $1,080. With a single payment the rate is 1,080 ÷ 980 − 1 = 10.20%. The quoted rate was 8%, since $80 of interest on $1,000.
2. A $12,000 loan over two years is quoted at a flat 5%. What are the total interest and the monthly payment, and is the true rate about 5%?
Show the working
Interest = 12,000 × 5% × 2 = $1,200. The total to repay is $13,200, so the payment is 13,200 ÷ 24 = $550. The borrower owes less and less during the two years, so interest is charged on money already repaid. Solving for the rate that makes 24 payments of $550 worth $12,000 gives about 9.3% a year, nearly double the flat 5%.
3. Offer A is a $10,000 two-year loan at 5% with a 4% fee. Offer B is the same loan at 5.5% with no fee. Which is cheaper if held to the end?
Show the working
Offer A has a payment of $438.71 and costs $929 in interest and fees, since the borrower receives $9,600. Its true yearly rate is about 9.03%. Offer B has a payment of $440.96 and costs $583, and its true rate is its quoted 5.50%. Offer B is cheaper by about $346, even though its rate is higher and its payment is $2.25 more a month.
4. Why does the same fee make a loan more expensive per year if it is repaid early?
Show the working
The fee is paid once at the start, so it does not shrink when the loan is repaid early. The same dollars are spread over a shorter time, so the yearly rate is higher. The interest, in contrast, is charged only for the time the money is out, so it falls with early repayment.
5. A lender advertises a loan with a lower rate than a competitor but a higher APR. What does this tell you?
Show the working
The lower rate comes with larger fees or other charges that the APR counts. Check how long you expect to keep the loan, since the fee matters most when the loan is short or repaid early, and compare the total cost in dollars.
Where this is used
- A borrower compares a bank loan, a car finance offer and a lender's online loan by APR and total cost.
- A small business owner works out the true cost of an invoice financing or merchant cash advance quoted as a fee.
- A regulator requires lenders to show the APR in the same way so that offers can be compared.
- A saver or investor uses the same discounting idea to find the return on any set of cash flows.
Key terms
- Interest rate
- The yearly cost of borrowing the money, before fees and other charges.
- Annual percentage rate (APR)
- A broader yearly measure that combines the interest rate with certain charges made to get the loan.
- Origination fee
- A charge made by the lender for setting up the loan, often taken from the amount paid out.
- Effective annual rate
- The yearly rate once the compounding of the monthly rate is counted.
- Flat rate
- A quote in which interest is worked out on the original amount for the whole term.
- Reducing-balance loan
- A loan in which interest is charged only on the amount still owed.
- Early repayment
- Paying off a loan before the end of its term.
- Net proceeds
- The cash the borrower actually receives, after fees.
Questions people ask
Why is the APR higher than the interest rate?
Because it counts the fees as well as the interest. If there are no fees and the loan runs to the end, the two are the same.
Is a loan with a fee always worse?
No. A loan with a fee and a lower rate can be cheaper if it is held for long enough. Compare total cost over the time you expect to keep the loan.
Why do lenders use flat rates?
A flat rate looks lower than the true rate, and it is easy to explain. Rules in many countries now require the APR to be disclosed as well.
Is the APR the same everywhere?
No. The idea is the same, but the exact method and the charges counted vary by country and product, so use the figure that the lender must give you under the rules where you live.
Sources and review
- Consumer Financial Protection Bureau, What is the difference between a loan interest rate and the APR?, for the definition of the interest rate and the annual percentage rate and the advice to compare APRs with APRs.
- Consumer Financial Protection Bureau, What is the difference between a mortgage interest rate and an APR?, for the charges included in the APR and the limits of the APR when loans differ in type or in how the rate can change.
How the numbers were checked: every payment, fee, interest total, APR and flat-rate equivalent in the lesson was recomputed in plain code, the true yearly rate was found by repeated halving until it was exact to many decimal places, and the calculator, which runs separately, was compared with that code across a grid of inputs. The loan is invented for teaching, and the flat-rate relationship is the author's own calculation from the formulas shown.