Einstein reportedly called compound interest the eighth wonder of the world. Whether or not he actually said that, the sentiment holds — compound interest is the most powerful force in personal finance, and most people understand it only vaguely. This guide explains it concretely, with numbers you can follow.
Simple interest is calculated only on the original principal. If you deposit $1,000 at 5% simple interest, you earn $50 every year. After 10 years you have $1,500.
Compound interest is calculated on the principal plus all previously earned interest. Your interest earns interest. The same $1,000 at 5% compounded annually: after year 1 you have $1,050. Year 2 you earn 5% on $1,050 — so $52.50. After 10 years you have $1,629. That extra $129 came from nothing except interest on interest.
At 10 years the difference is modest. At 30 years the same $1,000 at 5% compounded becomes $4,322 vs $2,500 simple. That's the compounding effect in full force.
The formula is: A = P(1 + r/n)nt
Example: $5,000 invested at 7% compounded monthly for 20 years. A = 5000 × (1 + 0.07/12)240 = $20,097. You turned $5,000 into over $20,000 without touching it.
The formula above assumes a one-time lump sum. In reality, most people invest steadily — a monthly contribution to an ISA, 401(k), or savings account. Adding regular contributions dramatically accelerates growth.
| Scenario | After 20 years | After 30 years |
|---|---|---|
| $5,000 lump sum, 7% compounded monthly, no contributions | $20,097 | $38,697 |
| $0 initial, $200/month, 7% compounded monthly | $104,185 | $243,994 |
| $5,000 initial + $200/month, 7% compounded monthly | $124,282 | $282,691 |
The $200/month scenario outperforms the lump sum by almost 5× over 20 years. This is why financial advisors talk about "paying yourself first" — consistency beats timing.
The Rule of 72 lets you estimate how long it takes money to double: divide 72 by the annual interest rate.
It's also useful in reverse: if inflation is 3%, your purchasing power halves in about 24 years. This is why leaving large sums in zero-interest accounts is quietly expensive over long periods.
The same mechanism that grows investments also grows debt. A $5,000 credit card balance at 20% APR, if you only pay the minimum each month, will take over 25 years to pay off and cost more than $12,000 in interest alone — more than double the original balance.
This is why financial advisors often say the best investment return is paying off high-interest debt: a guaranteed 20% "return" on every dollar you use to pay down a 20% APR card is extraordinarily hard to beat in the market.
The two levers that matter most are time and contribution consistency. Rate of return matters too, but it's the one you control least. What you can control: starting earlier, and making contributions automatic so you don't skip months.
Even modest amounts invested early outperform larger amounts started late. $200/month from age 25 to 65 at 7% compounds to about $525,000. The same $200/month started at 35 reaches only $243,000 — less than half — despite paying in for only 10 fewer years.
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