Compound Interest, Year by Year

Compound interest is interest earned on interest. The idea is simple, but its effect is easy to underestimate, because nothing much seems to happen for years and then the numbers start to move quickly. Following one deposit through time shows why.

One deposit, followed over 30 years

Put $1,000 into an account that earns 5 percent a year, compounded once a year, and never add to it or take anything out.

Year 1: you earn $50, for a balance of $1,050.
Year 2: you earn 5 percent of $1,050, which is $52.50, for $1,102.50. The extra $2.50 is interest on last year's interest.
Year 10: the balance is about $1,629. Interest that year is roughly $78.
Year 20: about $2,653. That year's interest is about $126.
Year 30: about $4,322. That single year adds around $206, four times what the first year did, from the same original deposit.

With simple interest, which is paid only on the original $1,000, the balance after 30 years would be $2,500. The gap of more than $1,800 is entirely the result of compounding.

The rule of 72

A quick way to estimate the effect is to divide 72 by the annual rate. The answer is roughly the number of years it takes money to double. At 5 percent, about 14 years. At 8 percent, about 9. At 2 percent, about 36. The rule is an approximation, but it is close enough to compare options in your head.

Why starting earlier matters more than starting bigger

Because growth accelerates over time, the years at the beginning matter most. Someone who invests $200 a month from age 25 to 35 and then stops will often end up with more at 65 than someone who invests $200 a month from 35 to 65, despite contributing a third as much, if both earn the same steady return. The early saver's money simply has more years to compound. Real returns vary from year to year and are not guaranteed, but the principle holds.

How often interest is added

Interest can be compounded yearly, monthly or daily. The more often it is added, the slightly faster the balance grows. That is why savings accounts in the US advertise an annual percentage yield, or APY, which includes the effect of compounding, so you can compare accounts fairly. For an account paying 5 percent compounded monthly, the APY is about 5.12 percent.

For those who like formulas, the balance after a number of years is the starting amount multiplied by (1 + r/n) raised to the power of n times t, where r is the annual rate, n is how many times a year interest is added and t is the number of years.

The same force, working against you

Compounding works on debt too. Most credit cards calculate interest daily on the outstanding balance, and unpaid interest becomes part of the balance that is charged interest the next day. Card rates are often above 20 percent a year, which by the rule of 72 means an unpaid balance can double in under four years. Paying the full statement balance each month avoids interest on purchases altogether, which is why high-interest debt is usually the first thing worth clearing before investing.

What to take from it

Compounding rewards time and consistency more than cleverness. Small amounts saved early, left alone and added to regularly tend to do more than larger amounts saved late. And the same arithmetic makes high-interest debt one of the most expensive things to carry.