Compound interest is when interest earns interest.
History's lessons for today's decisions ／ Calculate with Your Own Numbers
Calculating compound interest
With your principal and interest rate, how much will it become in how many years? In how many years will it double?
Compound Interest and the Rule of 72 in 3 Minutes
1See it
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Multiply the principal by (1 + the interest rate) for the number of years.
If you deposit $100 at 5 percent per year,
it becomes $105 after 1 year, and $110.25 after 2 years.
The Rule of 72. 72 ÷ interest rate = the approximate number of years it takes to double.
At 9 percent, it takes 8 years. At 1 percent, it takes 72 years.
This is a rule of thumb. Calculate the exact number of years with the compound interest formula.
Compound interest also works on the interest of money you borrow.
Check the interest rate for both your savings and your loans.
2In numbers
72years
Approximate years for principal to double at 1% per year
3What would you do?
You see information for savings and a loan side-by-side. Which one should you check for the compound interest rate?
Pick one
Only the savings information
Compound interest also works on the interest of money you borrow. You should check the interest rate for both savings and loans.
Both the savings and the loan
That's right. Compound interest works on both savings and loans. The power of time is just as strong when you're the one borrowing.
4Read more
When to use When you want to know the weight of the number of years by looking at deposit or loan interest rates.
Compound and simple interest
Compound interest is interest on interest. You multiply the principal by one plus the interest rate, raised to the power of the number of years. Simple interest is interest only on the principal. In an example from the U.S. Securities and Exchange Commission, if you deposit one hundred dollars at five percent per year, you will have one hundred and five dollars after one year, and one hundred and ten point two five dollars after two years.
The Rule of 72
Dividing seventy-two by the interest rate gives the approximate number of years it will take for the principal to double. At nine percent, it's eight years; at one percent, it's seventy-two years. This is a rule of thumb; the exact number of years is calculated using the compound interest formula.
It also works for borrowers
Compound interest also works on the interest of borrowed money. Check the interest rate for both deposits and loans.
Try with your own numbers
If you change the numbers, it recalculates on the spot. The formula is written below.
Input value
Output value
Balance with compound interest（Yen）—
Balance with simple interest（Yen）—
Interest on interest（Yen）—
Approximate years to double (Rule of 72)（years）—
Formula Balance with compound interest = Principal × (1 + Interest Rate ÷ 100) ^ Number of years. Balance with simple interest = Principal × (1 + Interest Rate ÷ 100 × Number of years). Approximate years to double = 72 ÷ Interest Rate
In other countries
The U.S. Securities and Exchange Commission teaches the same formula and the Rule of 72 in materials for classrooms. The Financial Services Agency calls the profit from reinvesting earnings into the principal "compound interest" and explains that its effect grows larger over longer periods. The formula does not change by country.
Bibliography
- What is compound interest? (Teachers, Classroom Resources)U.S. Securities and Exchange Commission, Investor.gov
- The basics of asset building (long-term, cumulative, and diversified investment).Financial Services Agency
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