Simple vs compound interest
The difference is small over a year and enormous over twenty. What separates the two, when each is used, and how to tell which one a product is quoting you.
Compare them on your own figuresThe mechanical difference
Simple interest is calculated on the amount you started with, for the whole term. Compound interest is calculated on the balance, which includes interest already earned. That is the entire distinction, and everything else follows from it.
Over one year at the same rate the two are identical. Over five they diverge noticeably. Over twenty-five the compound figure can be several times the simple one, which is why the term matters more than the rate when you are comparing them.
What the gap looks like
At 8% on 100,000, the difference is not a rounding error - it is most of the return.
| Term | Simple | Compounded | Difference |
|---|---|---|---|
| 1 year | 108,000 | 108,000 | 0 |
| 5 years | 140,000 | 146,933 | 6,933 |
| 10 years | 180,000 | 215,892 | 35,892 |
| 20 years | 260,000 | 466,096 | 206,096 |
| 30 years | 340,000 | 1,006,266 | 666,266 |
Which one you are being quoted
Deposits and investments almost always compound, and the product will say how often. Short-term personal loans, many late-payment terms and most informal lending are quoted simple, because the term is short enough that the difference is small and the arithmetic is easier to explain.
The one to watch is a loan quoted at a 'flat rate'. A flat rate is simple interest charged on the original amount for the whole term, even though you are paying the balance down every month - so the effective rate you are actually paying is close to double the number quoted. If a lender quotes a flat rate, ask for the reducing-balance equivalent before comparing it with anything.
Compounding frequency matters less than people think
Monthly compounding beats annual, and daily beats monthly, but the increments shrink fast. 100,000 at 10% for ten years reaches 259,374 compounded annually and 270,704 compounded monthly - about 4% more. Daily compounding adds barely anything on top of monthly.
A product advertising daily compounding at a slightly lower rate is almost always worse than a higher rate compounded annually. Compare the effective annual rate, which folds the frequency into a single comparable figure.