Entry I · The Library

How loan interest actually works

Almost every argument about whether a loan is expensive is really an argument about which number is being quoted. Interest rate and annual percentage rate are not synonyms, and the gap between them is where the money is.

Reference entry · Educational content · Not an offer of credit

A loan has two prices attached to it. The first is the interest rate: the periodic charge for the use of the money, expressed as an annual percentage of the outstanding balance. The second is the annual percentage rate, or APR: the total cost of the credit — interest plus the finance charges you paid to obtain it — expressed as a single annualised percentage. When those two numbers are far apart, fees are doing the work.

Section oneRate versus APR

Imagine two lenders both offering to lend you money for four years at ten per cent. The first charges nothing to originate the loan. The second deducts a four per cent origination fee from the amount advanced, so you sign for the full amount but walk away with less. Both loans carry a ten per cent interest rate. Only one of them costs ten per cent a year.

The APR is defined to catch exactly that. It asks: given the payments the borrower is committed to make, and given the amount the borrower actually received, what single annual rate makes those two things equal? Because the fee reduces the money you received but does not reduce your payments, the APR on the second loan comes out higher. This is why the Truth in Lending disclosure, the boxed table near the front of a consumer credit agreement, puts the APR first and in the largest type. It exists to make offers comparable in one glance.

Two cautions. First, an APR is only comparable across loans of the same term — a twelve-month loan and a sixty-month loan at the same APR are not equivalent commitments. Second, not every charge is a finance charge. Some fees, notably certain third-party costs, are excluded from the APR calculation by rule, which means the APR is a very good comparison tool and not a complete statement of everything a loan will cost you.

Section twoWhat amortisation does to a payment

On a fully amortising instalment loan, every payment is identical, but its composition is not. Interest is charged on the balance that is still outstanding. At the start the balance is large, so most of the payment is interest and only a small slice reduces the principal. As the balance falls, the interest portion falls with it, and the principal portion grows. By the final payments almost the whole instalment is principal.

That shape has a practical consequence people discover at the worst moment. Two years into a five-year loan, you have made forty per cent of the payments but you have not retired anything like forty per cent of the balance. If you sell the financed asset or refinance early, the payoff figure will be higher than a straight-line assumption suggests. This is normal and it is not a trick — it falls out of charging interest on the balance actually outstanding — but it surprises people every day.

Section threeWork it out yourself

The calculator below computes the level monthly payment on a fully amortising loan, then solves for the APR by treating any upfront fee as a reduction in the money advanced. Change the fee to zero and the APR collapses back to the interest rate; that equality is the clearest demonstration of what the APR is for. Nothing you type is sent anywhere — the arithmetic runs in your browser.

Try three experiments with it. Set the fee to zero and watch the APR meet the interest rate. Hold everything constant and stretch the term from thirty-six months to seventy-two, and watch the monthly payment fall while the total of payments climbs. Then hold the payment roughly constant by cutting the amount as you stretch the term, and see how much less loan the same money buys.

Section fourSimple, compound and precomputed interest

Three conventions cover most consumer lending, and they behave very differently when you pay early or late.

• Simple interest accrues daily on the outstanding principal. Most car loans and personal instalment loans work this way. Paying a few days early saves a few days of interest; paying late costs a few days more, and part of your next payment goes to catching up rather than to principal.
• Compound interest charges interest on accrued interest. It is the norm on revolving credit, where an unpaid balance carries forward and the next period's charge is calculated on principal plus the interest already added.
• Precomputed interest calculates the whole finance charge at the outset and builds it into the balance. Paying early does not automatically save the unearned portion; whether you get a rebate depends on the contract and on state law. If your agreement mentions a precomputed balance or a rebate method, read that clause twice.

Section fiveWhy the term costs more than the rate

Borrowers negotiate hard over a quarter of a percentage point and then accept an extra eighteen months without comment. That is backwards. Rate scales the cost; term multiplies the number of periods over which the cost is charged, and it also keeps the balance high for longer, which compounds the effect. Lengthening a loan is the single most reliable way to make a payment look affordable while making the loan expensive.

The reverse is also true and is the most under-used tool in consumer credit: shortening the term, or paying a fixed amount extra against principal each month, cuts total interest substantially more than most people expect. Use the calculator above with a shorter term and compare the total of payments.

Section sixFour expensive misreadings

1. Treating an advertised rate as your rate. Advertised pricing is normally the best tier available to the strongest applicants. Your tier depends on what the underwriter sees.
2. Comparing a monthly payment to a monthly payment. Two payments are only comparable when the amount and the term are the same. Otherwise compare APR and total of payments.
3. Assuming interest stops when you dispute something. It generally does not. Interest accrues on the balance until the balance is paid, whatever else is in progress.
4. Ignoring what the loan is secured by. Price is only half of a credit decision. The other half is what happens if it goes wrong, which depends on whether anything is pledged.

Section sevenWhere to go next

Once the pricing makes sense, the next question is why a lender offered you that price rather than another. That is underwriting, and it is more legible than most people assume — continue to what lenders look at in an application. If a term above was unfamiliar, the glossary defines it, and reading a loan agreement shows where each of these numbers physically appears in the document you will be asked to sign.