The sum, step by step
Moneysmart’s worked example takes $2,000 at 5% a year for two years, with interest added monthly, and solves it in three steps.
Find the rate for one period
Interest is added monthly, so the yearly 5% is divided by 12: 0.05 ÷ 12 = 0.00416667.
Count the periods
Two years of monthly additions: 2 × 12 = 24.
Grow the balance once per period
$2,000 is multiplied by (1 + 0.00416667) twenty-four times over, which gives $2,209.88.
Moneysmart’s working; recalculated for this guide to the same cent.
The two habits in that working carry over to any compound sum: the rate is the rate for one period, not for a year, and the count is of every period across the whole term. Interest of $209.88 on $2,000 is a little more than two years of 5% would give on the starting amount alone ($200), and the extra $9.88 is interest earned on interest. (This guide’s arithmetic, from Moneysmart’s example.)
Time does most of the work
Moneysmart’s second example puts $10,000 into an account paying 3% a year, compounded monthly, and leaves it there.
| Left for | Balance | Interest earned |
|---|---|---|
| 5 years | $11,616 | $1,616 |
| 10 years | $13,494 | $3,494 |
| 20 years | $18,208 | $8,208 |
Recalculated for this guide: $11,616.17, $13,493.54 and $18,207.55, which round to Moneysmart’s figures.
Read down the rows. The first five years earn $1,616.17; the next five earn $1,877.37; the ten years after that earn $4,714.01, against $3,493.54 in the first ten. In the example the rate never changes and nothing more is put in. What changes is the balance each later period starts from. (This guide’s arithmetic, from Moneysmart’s example.)
That is the reasoning behind Moneysmart’s advice to start saving early: the longer money is saved, the more the balance can grow.
Added monthly, or paid at the end
Moneysmart’s third example compares two people who each invest $10,000 at 5% for five years. One earns interest monthly; the other earns it at the end of the five-year term.
Worked here as simple interest, which reproduces Moneysmart’s $12,500.
The gap is $333.59, which Moneysmart rounds to $334.
Moneysmart puts the balances at $12,834 and $12,500, and says the extra $334 comes from earning interest on interest each month. Same money, same rate, same five years: only how often the interest is added has changed.
Compounding works for a borrower’s debt too
Moneysmart’s glossary defines compound interest as interest on the starting amount and on the interest already accumulated, on money borrowed or invested. The arithmetic in this guide does not care which side of it a person is on: on a debt that is not being paid down, interest charged on interest makes the balance grow by the same steps.
What a compound sum leaves out
Every sum on this page assumes a steady rate. Moneysmart sets bank deposits, which do not rise and fall in price like shares, beside shares, whose prices can fall quickly. Its questions to ask before investing start with how an investment could make or lose money, and include what it costs to buy, hold and sell.
Two things the calculator does not doMoneysmart describes its compound interest calculator as a model, not a prediction, and says its results are in future dollars, with no adjustment for inflation. It also leaves fees out, which is why Moneysmart has a separate managed funds fee calculator for checking how fees and costs affect an investment.
The next two exercises put those lines back into the sum: fees, then inflation.