Compound Interest Year by Year

1,000 dollars compounded annually at 3, 5 and 8 percent, tracked year by year to 30, plus rule-of-72 doubling times for each rate.

Compound interest adds earned interest back to the principal, so the interest earns its own interest in later periods. Starting with 1,000 dollars at 5 percent compounded annually, the balance reaches about 1,276 dollars after 5 years and about 1,629 dollars after 10. By year 20 it is about 2,653 dollars; by year 30, about 4,322 dollars.

At 3 percent the same 1,000 dollars reaches about 1,344 dollars in 10 years and about 2,427 dollars in 30. At 8 percent it reaches about 2,159 dollars in 10 years and about 10,063 dollars in 30. The rate difference looks modest on paper and dominates the result over decades.

The rule of 72 estimates doubling time without a calculator: 72 divided by the interest rate gives the approximate number of years for money to double. At 3 percent, about 24 years; at 5 percent, about 14 years; at 8 percent, about 9 years. At 6 percent, about 12 years. The rule is an approximation, accurate enough for planning.

The same arithmetic runs in reverse on debt. A credit card balance at 24 percent APR compounds against the borrower at the same pace the savings table runs in the saver's favour, which is why paying a card in full each month changes the outcome completely.

These figures assume annual compounding and no additional deposits. Monthly compounding produces slightly higher balances, and regular contributions change the curve far more than the compounding frequency does.

• Rule of 72: 72 ÷ rate = approximate years to double.
• At 3 percent, doubling takes about 24 years; at 5 percent, about 14; at 8 percent, about 9.
• Compounding works the same way on debt — in the lender's favour.

Further reading

• The 50/30/20 Split in Dollars
• APR vs APY, With Numbers