Compound Interest Explained with Real Numbers
Quick answer
Compound interest means earning interest on your interest, and how often it compounds changes the result even at the same stated rate. $25,000 at 7% for 15 years grows to $68,975.79 compounded yearly, but to $71,223.67 compounded monthly, which is $2,247.88 more from the compounding frequency alone. The "rule of 72" estimates how long money takes to double by dividing 72 by the interest rate. At 7% it gives 10.29 years against an exact 10.24, but at 15% it gives 4.80 years against an exact 4.96, and the gap grows the further the rate is from the rule's sweet spot.
Compound interest is usually summed up as "interest on interest". That's right, but it skips the part that really changes the outcome: how often the compounding happens. The same yearly rate gives different final balances depending on whether it compounds once a year, every month, or some other way.
This guide works through both effects with real numbers: the actual difference between yearly and monthly compounding at a realistic rate, and exactly how accurate the well-known "rule of 72" shortcut for doubling time really is.
The same rate, two different results
$25,000 invested at 7% a year for 15 years grows to $68,975.79 if interest is added once a year. If it's compounded monthly instead (the same 7% yearly rate, applied as roughly 0.583% each month), the same $25,000 grows to $71,223.67. That's $2,247.88 more, from the compounding frequency alone, with nothing else changed.
The difference comes from monthly compounding starting to earn interest on each month's interest straight away, rather than waiting a whole year for it to be added to the balance. The more often interest compounds, the closer you get to the theoretical maximum of continuous compounding. But the step from monthly to daily is much smaller than the step from yearly to monthly, because most of the benefit is already captured once compounding is monthly.
The rule of 72, and how far off it really is
The rule of 72 estimates how many years an investment takes to double: divide 72 by the yearly interest rate. At 7% it gives 72 ÷ 7 = 10.29 years, very close to the exact answer of 10.24 years, an error of only 0.04 years.
It isn't equally accurate everywhere, though. At 5% it gives 14.40 years against an exact 14.21, an error of 0.19 years, roughly four times as large. At 15% it gives 4.80 years against an exact 4.96, an error of 0.16 years the other way. The rule works best at around 7-8% and drifts further off the further the real rate is from there.
- Use the rule of 72 for a quick estimate in your head, not as a figure to plan a particular date around. At low or high rates the error is real, not tiny.
- The error changes direction: the rule overestimates the time to double at low rates and underestimates it at high ones.
- The Compound Interest Calculator works out the exact figure, rather than the rule-of-72 estimate, for any rate and any compounding frequency.
Frequently Asked Questions
Does compounding frequency matter as much as the interest rate itself?
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No. The rate itself is almost always the bigger factor, and compounding frequency adds a smaller effect on top. That effect isn't trivial over long periods, though, as the $2,247.88 example on $25,000 shows.
Is the rule of 72 accurate?
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It's a genuinely useful shortcut for doing in your head, and it's most accurate around 7-8% a year, where this guide's own example is off by only 0.04 years. At rates further from that range, in either direction, the error grows, so don't treat it as exact.
What compounding frequency do real savings accounts and investments use?
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It varies. Many savings accounts compound daily, many bonds and CDs compound twice a year or yearly, and most long-term investment returns are quoted as a yearly rate for simplicity, without any compounding frequency at all.
Why does more frequent compounding always help, never hurt?
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Because it can only add interest sooner, never later. At the same stated yearly rate, it either helps or leaves the result unchanged compared with less frequent compounding. It only ever works in one direction.