About the Compound Interest
Compound interest is interest earned on both the original principal and the interest already added to it. This compound interest calculator shows the total amount, the interest earned and the effective annual rate for any principal, rate and period, with a choice of how often interest is compounded: yearly, half-yearly, quarterly, monthly or daily.
Savers use it to understand how deposits and investments grow, students use it to check coursework, and borrowers use it to see how unpaid interest on a credit card or overdue loan can build up. Business owners find it useful for estimating the future value of reserves, or the real cost of finance when interest is capitalised rather than paid as it falls due.
The result depends on the principal, the annual rate, the time and the compounding frequency. The more often interest is compounded, the higher the effective annual rate, although the gain from moving beyond monthly compounding is small. Time has the largest effect: because growth is exponential, the later years add far more than the early ones. The calculation assumes a constant rate and no withdrawals.
How to use it
- 1Enter the principal amount and the annual rate of interest.
- 2Enter the time period in years; decimals are accepted.
- 3Choose how often interest is compounded.
- 4Read the total amount, the compound interest and the effective annual rate, and compare it with simple interest on the same terms.
How this is calculated
A = P × (1 + r ÷ n)^(n × t) P = principal, r = annual rate ÷ 100, n = number of times interest is compounded in a year, t = time in years. Compound interest = A − P. Effective annual rate = (1 + r ÷ n)^n − 1.
Frequently asked questions
What is the compound interest formula?
The amount equals the principal multiplied by one plus the rate per period, raised to the number of periods. The rate per period is the annual rate divided by the number of compounding periods in a year, and the number of periods is that frequency multiplied by the years. Compound interest is the amount minus the principal.
What is the effective annual rate?
It is the true yearly rate once compounding within the year is taken into account. A quoted rate of 8% compounded quarterly gives an effective annual rate of about 8.24%. It lets you compare products that quote the same nominal rate but compound at different frequencies.
How does the compounding frequency affect my returns?
More frequent compounding means interest is added to the principal sooner and starts earning interest earlier, so the final amount is higher. The difference between yearly and quarterly compounding is noticeable over long periods, while the difference between monthly and daily compounding is very small.
What is the Rule of 72?
It is a quick way to estimate how long money takes to double with annual compounding: divide 72 by the annual rate of return. At 8% a year money doubles in roughly nine years, and at 12% in roughly six. It is an approximation, and the calculator gives the exact figure.
Does compound interest work against borrowers?
Yes. When interest is not paid as it falls due, it is added to the outstanding amount and further interest is charged on it. This is how revolving credit card balances and overdue loans grow quickly. Paying at least the interest portion on time prevents compounding from working against you.