Interest, APR and why the headline rate hides the cost

Interest is the price of using someone else’s money for a period. The only thing that makes it confusing is that the price is usually quoted in a way that makes comparison hard, and the difference between the quoted figures is where most of the cost hides.

Two ideas do most of the work: compounding, which is interest charged on interest already added, and the annual rate convention, which decides whether two quoted rates are comparable at all.

Quick answer

A monthly rate tells you what interest is charged. The annual percentage rate tells you what the credit costs, including fees charged as part of it. Compare APR to APR, and never compare an APR to a monthly rate — they are different units.

Compounding, in one example

A balance charged at a simple rate grows in a straight line. A balance charged on the amount plus the interest already added grows on itself. Over one month the two are nearly identical. Over several years they are not close.

The doubling time of a compounding amount is roughly 72 divided by the percentage rate. At 6 per cent a year, money doubles in about twelve years; at 18 per cent it doubles in four. These are illustrative arithmetic rather than quoted rates — the point of the rule is that an 18 per cent revolving balance is a different kind of problem from a 6 per cent one, whatever the rates happen to be.

What an APR adds that a monthly rate leaves out

A monthly rate tells you what interest is charged. The annual percentage rate tells you what the credit costs, including fees charged as part of it. Those are different questions and only the second lets you compare two offers.

• Fees included. An arrangement fee raises the APR above the nominal rate, which is the point of the measure.
• Time included. The APR assumes a repayment schedule. Two products with identical rates can produce different APRs if one front-loads charges.
• Comparability. Because the convention is defined in law in most jurisdictions, two APRs from two lenders mean the same thing. Two “monthly rates” may not.

Fixed and variable, which is a question about who takes the risk

A fixed rate transfers the risk of rate changes to the lender, and you pay for that in the rate. A variable rate leaves the risk with you, which is cheaper while rates are stable and expensive when they rise.

For a short borrowing period the difference is small. For a long one it is the main variable in the whole arrangement, and the honest question is whether you could still afford the payment if the rate rose by several points.

The total cost, which is the number that matters

Multiply the payment by the number of payments and subtract the amount borrowed. That figure is what the credit costs in money, and it is the one to compare. APR is a rate for comparison; total cost is the amount you will actually pay.

Where a payment schedule is complex, or where the borrowing is long, the total is the only figure that cannot be presented flatteringly. It is also the figure most often absent from an advertisement.

Paying down faster, and where the saving comes from

Extra payments reduce the balance that interest is charged on, so the saving comes from every subsequent period rather than from the payment itself. This is why a modest overpayment early in a long arrangement saves more than a larger one late.

Check whether overpayment is permitted without a charge before relying on it. Then confirm which debt to attack first — the arithmetic is in debt problems and what to do, and the day-to-day structure in how to budget as a student.

Three numbers that are not the rate

The quoted rate is rarely the whole cost, and three other figures usually decide the answer.

• The total amount payable. Payments multiplied by their number. This is what the credit costs in money, and it cannot be presented flatteringly.
• The early repayment position. Whether settling early saves interest, and whether a charge applies. Some products include a fee that removes the benefit.
• The payment schedule. Whether payments are equal, or front-loaded with fees. Two products with the same rate and different schedules cost different amounts.

Short-term costs, which are the ones students actually meet

A shortfall covering a week is usually best solved by an overdraft, a payment arrangement, or by delaying the purchase. The relevant comparison is the cost of each against doing the thing a week later, and that third option is often cheapest and rarely considered.

Where borrowing is unavoidable, the cheapest form is usually the one with the lowest APR over the shortest period, not the one with the smallest payment. A longer term with a smaller payment almost always costs more in total, and advertising emphasises the payment.