Simple Interest Explained
Simple interest is calculated on the original amount only. Principal times rate times time, and nothing compounds. The Simple Interest Calculator does the arithmetic.
The formula and why it is predictable
Interest equals principal multiplied by the annual rate multiplied by the number of years. Lend 5,000 at 6 per cent for three years and the interest is 5,000 times 0.06 times 3, which is 900. The total repayable is 5,900.
That is the whole calculation, and its usefulness is that it is linear. Double the time and you double the interest. The amount owed in year three is exactly three times the amount owed in year one, which makes it the easiest interest to plan around and the easiest to check by hand.
Where it still applies
Short-term personal and business loans, often under a year, where compounding would make little difference anyway.
Many car loans and some consumer finance, particularly where the quoted structure is "flat rate".
Bonds paying a fixed coupon, where the payment is a percentage of face value and does not accumulate.
Some savings accounts, usually the less attractive ones, since compounding favours the saver.
And statutory or contractual interest on a debt or a late payment, which is commonly simple by law or by the terms.
Why the same rate is cheaper for the borrower
At the same quoted rate and term, simple interest always costs the borrower less than compound - because compound charges interest on interest already added.
Lend 10,000 at 7 per cent for ten years. Simple interest is 7,000, total 17,000. Compounded annually it is 9,672, total 19,672. Same rate, same term, 2,672 more. Over twenty years the gap more than triples.
Which means the quoted rate alone does not tell you the cost. The basis matters as much as the number, and the same percentage means two different things depending on it. The Compound Interest Calculator shows the other side.
The flat-rate trap
Worth knowing because it catches people on car and equipment finance. A flat rate charges simple interest on the full original amount for the whole term - even though you are repaying the principal as you go, so the balance is falling.
So a flat 6 per cent on a shrinking balance is roughly equivalent to an 11 or 12 per cent reducing-balance rate. The quoted number looks lower and the cost is higher. The comparable figure is the APR, which is what makes the two offers comparable at all.
Common questions
How do I handle part of a year?
Express the time in years - six months is 0.5, ninety days is 90 divided by 365.
Does the order of principal, rate and time matter?
No, multiplication commutes. Just keep the rate and the time in the same units.
Is simple interest ever better for a saver?
No. A saver always wants compounding, and more frequent compounding.
Which do most mortgages use?
Compound, applied monthly to a reducing balance - the Mortgage Calculator handles that case.
Need a simple interest figure?