Compound Interest
See how fast money grows when the interest earns interest too.
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Formula
How the calculation works
Compounding means each period's interest is added to the balance and then earns interest itself, so growth is multiplicative rather than a straight line. On 5,000 at 7%, simple interest adds 350 every year and reaches 8,500 after ten. Compounded yearly it reaches about 9,836, and the extra 1,336 is interest earned on interest, not on the original money.
The compounding frequency helps, but only modestly, because the growth factor is (1 + r/n)^n and that creeps toward a ceiling as n rises. Over the same ten years, yearly compounding gives 9,836, monthly gives 10,048, and daily gives 10,068. The whole span from yearly to daily is worth about 232, so switching an account from monthly to daily is not where the money is.
Time does more than the rate. The rough rule of 72, which is a convention rather than a law, divides 72 by the rate to get the doubling time: at 7% that is about ten years, which is why the ten-year figures roughly double the 5,000. Adding two percentage points of rate matters far less than adding ten years of patience.
Common mistakes
- Treating the compounding frequency as a detail. Over ten years on 5,000 at 7%, yearly compounding gives 9,836 and monthly 10,048; that 212 difference is real money, not rounding.
- Typing the rate as a decimal. The box wants 7 for seven percent; 0.07 computes a hundredth of the intended rate and makes the result look like a loss.
- Reading a nominal rate as the real return. 7% compounded monthly is about 7.23% a year once interest on interest is counted, and inflation is not deducted here at all.
When to use it
- Use it to see what a lump sum becomes over a long horizon, to compare two accounts that differ only in how often they compound, or to check the rough doubling time of an investment.
- It is the wrong tool once you add money every month; for that use the savings-with-deposits tool. And because it models no tax and no inflation, the figure it gives is a nominal one, not what the money will buy.
Worked example
5,000 at 7% monthly-compounded for ten years becomes 10,030.
Common questions
Does monthly compounding matter?
Yes, but modestly: over ten years yearly compounding gives about 9,836 against 10,030 monthly. More frequent compounding helps slightly.
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