Interest is the price of using someone else’s money. How it is calculated makes a real difference to what you earn on savings or pay on a loan, and there are two methods: simple and compound.
Simple interest
Interest is worked out on the original amount only. It is the same every period.
P is the principal, R the annual rate as a decimal and T the time in years. $10,000 at 5% for 10 years earns $10,000 × 0.05 × 10 = $5,000, for a total of $15,000.
Compound interest
Interest is added to the balance, and the next lot of interest is worked out on the new, larger balance. You earn interest on your interest.
PV is the starting amount, i the annual rate, n the number of times interest is added each year and t the number of years. $10,000 at 5% compounded annually for 10 years grows to $10,000 × 1.05^10 = $16,288.95.
Side by side
$10,000 at 5% a year, compounding annually:
| After | Simple | Compound | Difference |
|---|---|---|---|
| 1 year | $10,500 | $10,500 | $0 |
| 5 years | $12,500 | $12,763 | $263 |
| 10 years | $15,000 | $16,289 | $1,289 |
| 20 years | $20,000 | $26,533 | $6,533 |
| 30 years | $25,000 | $43,219 | $18,219 |
After one year there is no difference. The gap opens slowly and then widens faster each year, which is why time matters more than anything else with compounding.
The rule of 72
A quick estimate of how long money takes to double with compound interest: divide 72 by the interest rate. At 5% it takes about 72 ÷ 5 = 14.4 years. At 8%, about 9 years.
Where you will see each one
- Simple: short-term loans, some term deposits that pay at maturity, interest charged on overdue invoices.
- Compound: savings accounts, home loans, credit cards, superannuation and most investments.
Compounding works for you when you are saving and against you when you are borrowing. On a credit card at 20%, an unpaid balance doubles in under four years.
Run your own numbers with the simple interest calculator or the compound interest calculator.