APR versus simple interest cost:
formula and worked example

Two ways of stating the price of a loan

A lender can describe the cost of borrowing in more than one way, and the numbers rarely match. Simple interest charges the rate on the original amount for the whole time, regardless of how much has been repaid. The annual percentage rate, or APR, is a standardised yearly cost figure that, depending on the rules in a country, can also take certain fees into account. Knowing the difference stops a loan with a friendly-looking rate from costing more than expected.

The formula here gives the simple interest cost, the total interest on the original principal over the full term. It is a clean baseline: easy to compute, easy to explain, and a useful yardstick against which to compare the quoted offer.

Both figures are legitimate in the right place. Simple interest is a fair description of a short loan repaid in one payment, such as a bridge loan, or an interest-only arrangement. It becomes misleading only when it is used to describe a loan repaid in instalments.

Where lenders quote a flat rate but you repay in monthly instalments, the gap between that flat figure and the true yearly cost is where borrowers often get caught.

The formula and its three inputs

• Principal: the amount borrowed, in currency, on which interest is charged throughout.
• Rate: the annual interest rate as a decimal; 0.12 is 12% a year.
• Years: the term of the loan in years; for months, divide by 12.

Cost grows in a straight line with each input. Double the principal, the rate or the term, and total interest doubles. That linearity is exactly what makes simple interest easy to read, and also what makes it different from loans repaid by instalments.

Worked example: 250,000 at 12% for two years

1. 1Take the principal: 250,000.
2. 2Convert the rate to a decimal: 12% = 0.12.
3. 3Multiply principal by rate for one year of interest: 250,000 × 0.12 = 30,000.
4. 4Multiply by the number of years: 30,000 × 2 = 60,000.

You would repay 310,000 in total: the 250,000 borrowed plus 60,000 of interest. Spread over 24 monthly instalments, that is about 12,917 a month.

Why 12% flat is not 12% a year

Here is the catch. In the example above, if the 310,000 is repaid in 24 equal monthly instalments, you are not borrowing 250,000 for the whole two years. Each instalment returns part of the principal, so the amount you actually owe keeps falling, yet interest was calculated on the full amount throughout. The rate that equates the instalments with the amount borrowed works out to roughly 21.6% a year (nominal, monthly compounding), well above the 12% headline.

This is the distinction between a flat rate and a reducing-balance rate. A flat rate applies to the original sum, while a reducing-balance rate applies to what remains. The same advertised figure gives a much higher true cost under the flat method, which is why the quoted rate must be matched with how interest is applied.

A useful sanity check is the last instalment. On a reducing-balance loan, the final instalments are mostly principal, with very little interest in them. On a flat-rate loan the interest portion of each instalment stays the same from the first to the last, and that signals you are paying interest on money you no longer owe.

How the cost scales

The table increases the principal by 10% with rate and term unchanged.

Interest rises by exactly 10%, from 60,000 to 66,000, because cost is proportional to principal. The same holds for term and rate: three years at 12% costs 90,000, and a rate of 11% over two years costs 55,000. Cutting the term is often the most powerful lever, since each year removed takes out a full 30,000 here.

Where borrowers get misled

• Comparing a flat rate with an APR. They describe different things and cannot be set side by side without converting.
• Ignoring fees. Processing charges, insurance or documentation costs that are not in the interest figure raise the total cost.
• Assuming a flat rate behaves like a reducing-balance rate. Under a flat rate interest keeps being charged on the full principal even as the balance is paid down.
• Overlooking prepayment terms. Paying off early may save less than expected if interest was pre-calculated on the full term.

Early repayment is another place where the structure matters. With a reducing-balance loan, settling early saves the interest for the months not used. With flat interest or pre-calculated charges, the saving can be small unless the contract gives a rebate, so read the foreclosure terms before assuming that clearing the loan quickly will cut the cost.

A quick way to test any loan offer

1. 1Multiply principal by quoted rate by years to get the headline interest.
2. 2Add all fees and charges to get the total cost of credit.
3. 3Divide by the amount received and the years for an average yearly cost.
4. 4Ask the lender for the effective annual rate on a reducing-balance basis and compare.

If the effective rate is far above the quoted one, the loan is flat-rate or fee-heavy, and a different product may be cheaper.