The Compound Interest Calculator below can be used to compare and convert interest rates across different compounding periods. Please use our Interest Calculator to calculate compound interest.

What is compound interest?

Interest is the cost of borrowing money, or, more specifically, the amount a lender receives for advancing funds to a borrower. When paying interest, the borrower typically pays a proportion of the principal (borrowed amount). There are two types of interest: simple interest and compound interest.

Simple interest is interest earned solely on the principal, usually expressed as a percentage of the principal. To calculate an interest payment, multiply the principle by the interest rate and the number of periods for which the loan is active. For example, if one individual borrowed $100 from a bank at a simple interest rate of 10% per year for two years, the interest would be calculated as follows:

$100 × 10% × 2 years = $20

Simple interest is hardly utilised in the actual world. Compound interest is commonly employed instead. Compound interest is defined as interest earned on both the principal and the accumulated interest. For example, if one individual borrowed $100 from a bank at a compound interest rate of 10% per year for two years, at the conclusion of the first year, the interest would be:

$100 × 10% × 1 year = $10

At the end of the first year, the loan balance is principal plus interest, or $100 + $10, for a total of $110. The compound interest for the second year is calculated using the balance of $110 rather than the principal of $100. Thus, the second year’s interest would be calculated as:

$110 × 10% × 1 year = $11

The total compound interest after two years is $10 + $11 = $21, compared to $20 for simple interest.

Because lenders gain interest on interest, their earnings accumulate over time like an exponentially increasing snowball. As a result, compound interest can provide lenders with substantial financial rewards over time. The longer interest compounded on any investment, the larger the increase.

As an example, suppose a 20-year-old guy invests $1,000 in the stock market at a 10% annual return rate, which has been the average rate of return for the S&P 500 since 1920. When he retires at 65, the fund will be worth $72,890, or roughly 73 times his initial contribution!

While compound interest is efficient at increasing wealth, it may also be detrimental to debtors. This is why compound interest is sometimes referred to as a double-edged sword. Delaying or prolonging outstanding debt can significantly increase the total interest owed.

Different compounding frequencies

Interest can compound at any frequency, but it commonly compounds annually or monthly. Compounding frequency affects the amount of interest owed on a loan. For example, a loan with a 10% interest rate compounded semi-annually has an interest rate of 10% divided by two, or 5% every half-year. For every $100 borrowed, the interest for the first half of the year comes to:

$100 × 5% = $5

In the second half of the year, interest increases to:

($100 + $5) × 5% = $5.25

The total interest is $5 plus $5.25, which equals $10.25. As a result, a 10% interest rate compounded semiannually is comparable to a 10.25% interest rate compounded annually.

The interest rates on savings accounts and Certificates of Deposit (CDs) compound annually. Mortgages, home equity loans, and credit card accounts typically compound regularly. Furthermore, compounded interest rates appear lower. Because of this, lenders frequently prefer to offer interest rates compounded monthly rather than annually. For example, a 6% mortgage interest rate translates into a monthly interest rate of 0.5%. However, after compounding monthly, interest equals 6.17% compounded annually.

Our compound interest calculator above allows you to convert between daily, biweekly, semi-monthly, monthly, quarterly, semi-annual, annual, and continuous (meaning an unlimited number of periods) compounding frequencies.

Compound Interest Formulas

Compound interest can be calculated using sophisticated formulas. Our calculator provides a straightforward answer to that problem. However, individuals who seek a deeper grasp of how the computations work might refer to the formulas listed below.

Basic compound interest

The fundamental formula for compound interest is as follows.

At = A0(1 + r)n

where:

A0: the main amount, or initial investment.

At the quantity after time. t r: Interest Rate

n: number of compounding periods, typically expressed in years.

In the scenario below, a depositor creates a $1,000 savings account. It provides a 6% APY compounded once a year for the next two years. Use the equation above to find the total due upon maturity.

At = $1,000 × (1 + 6%)2 = $1,123.60

where:

A0: the main amount, or initial investment.

At: amount after time t, n: number of compounding periods each year.

r = interest rate.

T: number of years.

Assume the $1,000 in the previous example’s savings account has a daily compounded interest rate of 6%. This works out to a daily interest rate of:

6% ÷ 365 = 0.0164384%

Depositors can determine the following total account value after two years by using the above calculation to the daily interest rate:

At = $1,000 × (1 + 0.0164384%)(365 × 2)

At = $1,000 × 1.12749

At = $1,127.49

As a result, if a $1,000 savings account with a 6% compounded daily interest rate matures after two years, it will be worth $1,127.49.

Continuous Compound Interest

Continuous compounding interest reflects the mathematical limit that compound interest can reach within a certain time period. The continuous compound equation is expressed by the equation shown below:

At = A0ert

where:

A0 : principal amount, or initial investment

At : amount after time t

r : interest rate

t : number of years

e : mathematical constant e, ~2.718

For example, we wanted to calculate the maximum amount of interest that might be earned on a $1,000 savings account over two years.

Using the equation above:

At = $1,000e(6% × 2)

At = $1,000e0.12

At = $1,127.50

The examples demonstrate that the shorter the compounding frequency, the larger the interest earned. However, above a certain compounding frequency, depositors only get modest benefits, especially on smaller sums of principle.

Rule of 72

The Rule of 72 is a shortcut for calculating how long it will take a specific amount of money to double given a fixed annual compounding rate. It can be used for any type of investment as long as the fixed rate and compound interest are within a suitable range. Simply divide 72 by the yearly rate of return to find out how many years it will take to double.

For example, $100 with a fixed rate of return of 8% will take approximately nine (72 / 8) years to reach $200. Keep in mind that “8” represents 8%, thus users should avoid converting it to decimal form. As a result, the calculation would be done with “8” rather than “0.08”. Remember that the Rule of 72 is not an accurate estimate. Investors should treat it as a quick, approximate estimate.

History of Compound Interest

Ancient texts show that two of human history’s first civilisations, the Babylonians and Sumerians, used compound interest around 4400 years ago. However, their application of compound interest differs greatly from the approaches commonly utilised today. In their application, they accumulated 20% of the principal amount until the interest equalled the principal, after which they added it to the principal.

Historically, rulers recognised simple interest as legal in most circumstances. Certain societies, however, did not recognise compound interest as legal, labelling it usury. Compound interest, for example, was banned by Roman law and is recognised as a sin in Christian and Islamic writings. Nonetheless, lenders have utilised compound interest since mediaeval times, and it became more popular with the invention of compound interest tables in the 1600s.

Another factor that popularised compound interest was Euler’s Constant, or “e.” Mathematicians define e as the maximum mathematical value that compound interest can achieve.

In 1683, Jacob Bernoulli found the value of e while researching compound interest. He knew that having more compounding periods within a given finite period resulted in faster primary increase. It didn’t matter if the intervals were measured in years, months, or another unit of measurement. Each extended time resulted in better returns for the lender. Bernoulli also discovered that this series eventually approaches a limit, e, which specifies the relationship between the plateau and the interest rate when compounded.

Leonhard Euler later discovered and called the constant e, which equals roughly 2.71828. For this reason, the constant is named after Euler.