How compound interest works
Interest is added to the balance, and the next interest is earned on the bigger balance, so growth speeds up over time. With no additions:
Balance = P × (1 + r ÷ n)^(n × t)
P is the starting amount, r the yearly rate as a decimal, n how many times a year interest is added and t the number of years. With regular additions the calculator adds each one in its month and lets it grow from there.
10,000 at 5% for 10 years
Worked out by this calculator. More frequent compounding earns a little more:
| Compounded | Balance | Interest |
|---|---|---|
| Yearly | 16,288.95 | 6,288.95 |
| Quarterly | 16,436.19 | 6,436.19 |
| Monthly | 16,470.09 | 6,470.09 |
| Daily | 16,486.65 | 6,486.65 |
Adding 100 at the end of every month for 10 years at 5%, compounded monthly, grows to 15,528.23 from 12,000.00 paid in.
The rule of 72
A quick way to see how long money takes to double: divide 72 by the yearly rate. It’s close for everyday rates:
| Rate | Rule of 72 | Exactly (yearly compounding) |
|---|---|---|
| 3% | 24 years | 24 years |
| 6% | 12 years | 12 years |
| 9% | 8 years | 9 years |
AER and APY
Savings accounts quote the AER (in the US, the APY): the yearly rate after compounding, so accounts that pay interest monthly and yearly can be compared. The calculator shows it as the effective yearly rate.
How to read the result
- After so many years: the balance at the end; 5,000 plus 200 a month at 5% for 10 years grows to 39,291.50.
- Interest earned and its share of the total: how much of the balance the interest did.
- Effective yearly rate: the AER (or APY), for comparing accounts that compound differently.
Common mistakes
- Typing a monthly rate where a yearly one is wanted: the rate is a year.
- Forgetting tax and inflation: the figures are before both.
- Treating an expected investment return as guaranteed.
How to use it
- Type a starting amount, an amount to add, and whether you add it every month or every year.
- Type the yearly interest rate and how often interest is added.
- Choose how many years, and whether additions go in at the start or end of each period.
- Open the year-by-year table to see the interest each year.
Questions
How much will 10,000 grow to in 10 years?
At 5% compounded monthly, 16,470.09; compounded yearly, 16,288.95.
Does it take account of tax or inflation?
No. The figures are before tax and in today’s money. With inflation at a few per cent a year, what the balance will buy grows more slowly than the balance.
Is investment growth guaranteed?
No. For investments, type a rate you expect, not a promise: real returns go up and down, and investments can fall in value.
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