Compound interest works by calculating interest on your starting balance and the interest you’ve earned in previous periods. Say you start with $1,000 in your bank account (the initial principal) with a 5% annual compounding interest rate. After one year, your balance is $1,050. After two years, your balance is $1,102.50. How did this happen?
- Year one: $1,000 (starting balance) + $50 (5% interest on starting balance) = $1,050
- Year two: $1,050 (starting balance) + $52.50 (5% interest on balance including year one interest) = $1,102.50
In addition to earning $50 each year to keep a balance of $1,000, you also earn interest on your interest. So, you earned $50 from your first year of interest, $50 for the second year of interest, and $2.50 of interest on your interest. If the interest were not compounded, you would have earned just $50 the first year and $50 the second year.
Compound interest formula
How do you calculate compound interest? Here’s what the formula looks like:
A = P * (1 + r/n)nt
A refers to the total amount at the end of the investment period. On the other side of the equal sign, here’s what all those symbols mean:
- P (principal amount): The amount you invest initially, such as the starting balance of a high-yield savings account.
- r (interest rate): This is the interest rate on the account, expressed as a decimal. For instance, a 5% interest rate would appear in the compound interest formula as 0.05.
- n (number of times interest is applied): The compounding frequency refers to how often interest is compounded. For many accounts, it’s annual – that’s once a year. Some accounts may compound twice a year, quarterly, or even monthly. The higher the number of compounding periods, the more interest you stand to earn.
- t (total time): This should be expressed in years and refers to the length of time that money will be invested.
When calculating compound interest to determine the future value of your investment or savings, you need to know the compound period. The compounding period is the time between when the interest was last compounded and when it will be compounded again. In other words, it’s how often you earn interest. Compounding interest periods are often yearly.
The rule of 72
Want to know how long it will take you to double your money with compound interest? Just use the rule of 72.
With this rule, you simply divide the number 72 by the compound interest rate you’ll earn in an account. The result of the calculation is the number of years it will take to double your investment.
For instance, a 5% interest rate would take 14.4 years to double the investment: 72/5 = 14.4 years.
This formula is specifically helpful for compound interest that compounds annually. If you have continuous compounding interest, you should use the number 69.3.
