Compound Interest Calculator
Compound interest: what is it?
The cost of using borrowed funds, or more precisely, the sum that a lender gets paid for making an advance to a borrower, is known as interest. The borrower will typically pay a portion of the principal (the amount borrowed) in interest. There are two types of interest: simple interest and compound interest.
Simple interest, which is typically expressed as a predetermined percentage of the principal, is interest generated solely on the principal. Simply multiply the principle by the interest rate and the number of periods the loan is in effect to calculate the interest payment. For instance, if someone borrowed $100 from a bank for two years at a basic interest rate of 10% annually, at the conclusion of the two The interest would be revealed as:
$20 (100 × 10% × 2 years).
In the real world, simple interest is rarely utilized. Instead, compound interest is frequently used. Interest generated on both the principal and the accrued interest is known as compound interest. For instance, if someone borrowed $100 from a bank for two years at a compound interest rate of 10% annually, the interest at the conclusion of the first year would be:
$10 is $100 × 10% × 1 year.
The loan balance at the conclusion of the first year is $110, which is equivalent to $100 + $10 (principal plus interest). Rather than using the $100 principal, the second year’s compound interest is computed using the balance of $110. Consequently, the second year’s interest would equal:
$11 (110 × 10% × 1 year)
After two years, the total compound interest is $10 + $11 = $21, as opposed to $20 for simple interest.
Earnings compound over time like an enormously increasing snowball because lenders gain interest on interest. As a result, compound interest has the potential to provide lenders with substantial financial rewards over time. For every investment, the growth increases with the length of time the interest compounded.
For instance, a twenty-year-old guy put $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 the 1920s. The fund will increase to $72,890 when he retires at age 65, which is over 73 times the original investment!
Compound interest is a useful tool for increasing wealth, but it can also operate against debt holders. For this reason, compound interest can also be thought of as a two-edged sword. The total amount of interest due can rise significantly if outstanding debt is postponed or prolonged.
Interest can compound on any given frequency schedule but will typically compound annually or monthly. Compounding frequencies impact the interest owed on a loan. For example, a loan with a 10% interest rate compounding semi-annually has an interest rate of 10% / 2, or 5% every half a year. For every $100 borrowed, the interest of the first half of the year comes out to:
$100 × 5% = $5
For the second half of the year, the interest rises to:
($100 + $5) × 5% = $5.25
$5 + $5.25 = $10.25 is the total amount of interest. As a result, an interest rate of 10% compounded semi-annually is equal to an interest rate of 10.25% compounded annually.
Certificates of Deposit (CD) and savings account interest rates typically compound every year. Credit card accounts, home equity loans, and mortgage loans often compound once a month. Additionally, a higher frequency of compounding makes an interest rate appear smaller. Because of this, lenders frequently prefer to show monthly compound interest rates rather than annual ones. A 6% mortgage interest rate, for instance, translates to a 0.5% interest rate per month. Nevertheless, interest comes to 6.17% compounded annually after monthly compounding.
The conversion between daily, bi-weekly, semi-monthly, monthly, quarterly, semi-annual, annual, and continuous (i.e., an unlimited number of periods) compounding frequencies is supported by the compound interest calculator above.
Formulas for compound interest
Complex formulas may be used to calculate compound interest. Our calculator offers a straightforward way to deal with that challenge. Nonetheless, the following formulas might be used by individuals who wish to have a better grasp of how the computations operate:
Simple compound interest
The following is the fundamental compound interest formula:
At = A0(1 + r)n
where:
A0: the initial investment, or main amount
At: quantity following time tr: rate of interest
n: the quantity of compounding periods, typically stated in years
A $1,000 savings account is opened by a depositor in the example that follows. For the following two years, it offers an annual percentage yield (APY) of 6% compounded once. To determine the total amount owed upon maturity, use the calculation above:
$1000 × (1 + 6%)2 = $1,123.60
Prospective depositors should consult the formula below for various compounding frequencies (e.g., monthly, weekly, or daily).
where:
A0: the initial investment, or main amount
At: sum after time tn: number of annual compounding periods
r: interest rate
t: number of years
Assume that 6% interest compounded daily is included in the $1,000 in the savings account from the preceding example. This equates to the following daily interest rate:
Six percent ÷ 365 = 0.0164384%
Depositors can use the aforementioned calculation to get the entire account value after two years by using that daily interest rate:
365 × 2 = $1,000 × (1 + 0.0164384%)
$1,00 × 1.12749
At $1,127.49
At the end of two years, a $1,000 savings account with a 6% interest rate compounded daily will have grown to $1,127.49.
Constant compound interest
The mathematical maximum that compound interest can achieve in a given time frame is represented by continuously compounding interest. The following equation represents the continuous compound equation:
At = A0ert
where:
A0: the initial investment, or main amount
At: quantity following time tr: interest rate
t: years e: mathematical constant e, approximately 2.718
For example, we wanted to know how much interest we could receive in two years on a $1,000 savings account.
Using the previously mentioned equation:
$1,000e(6% × 2) at
At $1,000e0.12
At $1,127.50
The examples demonstrate that interest earned increases with a shorter compounding frequency. However, depositors only get modest benefits above a certain frequency of compounding, especially on smaller sums of capital.
The 72-rule
With a set return rate that accumulates annually, the Rule of 72 provides a quick way to calculate how long it will take for a given sum of money to double. Any investment that has a fixed rate and compound interest within a suitable range can use it. To find out how many years it will take to double, just divide 72 by the annual rate of return.
For instance, it will take roughly nine (72 / 8) years for $100 to grow to $200 with a fixed rate of return of 8%. Remember that “8” stands for 8%, so users shouldn’t convert it to decimal. Therefore, “8” rather than “0.08” would be used in the computation. Additionally, keep in mind that the Rule of 72 is not a precise computation. It should be used by investors as a fast, approximate estimate.
Compound Interest History
Compound interest was originally utilized approximately 4400 years ago by the Babylonians and Sumerians, two of the oldest civilizations in human history, according to ancient writings. Their use of compound interest, however, was far different from what is currently commonly employed. 20% of the principal was accumulated in their application until the interest and principal were equal, at which point the interest was added to the principal.
In the past, monarchs considered basic interest to be generally lawful. However, some communities did not consider compound interest to be as legitimate and instead referred to it as usury. For instance, compound interest was deemed a sin in both Christian and Islamic writings, and it was also forbidden by Roman law. However, compound interest has been utilized by lenders since the Middle Ages, and its use expanded in the 1600s when compound interest tables were developed.
Compound interest was also made prominent by Euler’s Constant, or “e.” E is the mathematical maximum that compound interest can achieve, according to mathematicians.
In 1683, Jacob Bernoulli made the discovery of e while researching compound interest. He realized that the principal grew more quickly when there were more compounding periods inside a given finite period. Whether the intervals were measured in years, months, or any other unit of measurement was irrelevant. The lender’s returns increased with each extra period. Additionally, Bernoulli noticed that this pattern eventually came close to a limit, e, which characterizes the connection between the interest rate and the plateau during compounding.
Later, Leonhard Euler found that the constant was roughly 2.71828 and gave it the name e. The constant is named after Euler as a result.