The Power of Compound Interest: Why $100 a Month Started Early Can Beat Almost Anything

Compound interest is simple to describe: you earn a return, and then you earn a return on that return. What is hard to grasp is how lopsided it becomes over time. For years it seems to do almost nothing. Then, late in the story, it does nearly all the work.

Same $100 a Month, Very Different Result

Take two savers. Each puts away $100 a month, earns 6% a year, and stops at age 65. One account is started for a child at age 5. The other is started by an adult at age 40.

	Started at 5	Started at 40
Years of saving	60	25
Total put in	$72,000	$30,000
Value at 65	$705,428	$69,299
Growth earned	$633,428	$39,299
Share of the final value that is growth	90%	57%

The child put in 2.4 times as much money and ended up with about ten times as much. Those extra 35 years of $100 a month cost $42,000 and produced an extra $636,129.

$100 a month at 6% a year, compounded monthly. The dashed line is the money actually deposited. Everything above it is growth.

The Last 10 Years Do the Heavy Lifting

Look at the same account in 10-year stretches. In the first decade it grows by about $16,388. In the final decade, with the same $100 a month going in, it grows by $326,709.

Growth of the age 5 account in each 10-year stretch, including the deposits made in that stretch.

That last decade alone produces 46% of the final balance. At age 65 the account earns about $3,527 a month in growth, more than 35 times the $100 going in. This is why stopping early, or cashing out in the final years, costs so much more than most people expect.

What It Takes to Catch Up

Time is very expensive to buy back. To reach the same $705,428 by 65 at the same 6%:

If you start at	You need to save each month
5	$100
20	$256
30	$495
40	$1,018
50	$2,426

None of this means it is too late at 40 or 50. $69,299 is more than double the $30,000 that went in, and 15 years of saving still adds real money. It simply means that whatever your age, the best month to start is this one.

The Rule of 72 and the Rule of 144

These are two of the most useful shortcuts in finance, and you can do them in your head. At 6%, money doubles in about 12 years (72 ÷ 6) and quadruples in about 24 years (144 ÷ 6). The second rule is really the first one twice: double, then double again.

Annual return	Rule of 72: years to double	Rule of 144: years to quadruple
3%	24	48
4%	18	36
6%	12	24
8%	9	18
12%	6	12

Run it backward too: if you have 24 years until you need the money, you need about 6% a year for it to quadruple. The same shortcut works against you. Debt at 18% doubles in about 4 years if nothing is paid, and inflation at 3% cuts your buying power in half in about 24 years.

For Those Who Like the Math

If you enjoy seeing how it works underneath, here are the formulas behind every number above.

Growth of a lump sum. A single amount P at a rate r per period for n periods grows to:

FV = P (1 + r)ⁿ

The exponent is the whole story. Time is not multiplied, it is an exponent, which is why the curve bends upward instead of rising in a straight line.

Regular monthly savings. Each deposit compounds for a different length of time, and adding them up gives a geometric series with a tidy answer:

FV = PMT × [ (1 + i)ⁿ − 1 ] ÷ i

Here PMT is $100, i is the monthly rate (0.06 ÷ 12 = 0.005) and n is the number of months (720). That gives $100 × [(1.005)⁷²⁰ − 1] ÷ 0.005 = $705,428.

The stated rate is not the real rate. 6% compounded monthly is actually (1.005)¹² − 1 = 6.17% a year. The more often interest compounds, the higher the true rate, up to a limit of e^0.06 − 1 = 6.18% with continuous compounding. This is the same reason a credit card at 19.99% really costs about 21.9% a year.

Why 72 works. Money doubles when (1 + r)^t = 2, so t = ln(2) ÷ ln(1 + r). Since ln(2) is about 0.693 and ln(1 + r) is close to r, the exact number is near 69. We use 72 because it divides evenly by so many rates, and it is a closer fit at typical returns. Here the exact answer at 6% compounded monthly is ln(2) ÷ ln(1.005) = 139 months, or 11.6 years. For 144, ln(4) is twice ln(2), so the answer is exactly double: 278 months, or 23.2 years.

The tipping point. Each month the account earns i × balance. That equals your $100 deposit when the balance reaches $100 ÷ 0.005 = $20,000, which happens at month 139, the same moment your money would double. From then on, growth adds more each month than you do. It gets a little neat: the tipping point is always at the doubling time, whatever the deposit or the rate.

What Changes the Result

Small differences in the rate matter a great deal over long periods. Here is the same $100 a month:

Annual return	25 years	60 years
3%	$44,601	$201,443
5%	$59,551	$455,058
6%	$69,299	$705,428
8%	$95,103	$1,778,853

This cuts both ways. Fees compound exactly the same way returns do, only against you, and so does tax on growth. That is why low costs and accounts such as the TFSA and RRSP matter so much over a lifetime. Inflation also shrinks what the final number will buy, so a large figure 60 years from now is worth much less in today’s dollars.

Where to Start

Set up an automatic monthly amount, even a small one, into an account suited to your goal and timeline, and increase it when your income rises. If you have children or grandchildren, a small monthly amount started early may be one of the most valuable gifts you can give. The hardest part is not the math. It is leaving the money alone long enough for the last ten years to arrive.

These examples are hypothetical and use a constant 6% return, compounded monthly, before fees, taxes and inflation. They are for illustration only. Actual returns vary from year to year, are not guaranteed, and may be negative.