On what sum of money will the compound interest for 2 years at 5% per annum?

home / financial / compound interest calculator

The Compound Interest Calculator below can be used to compare or convert the interest rates of different compounding periods. Please use our Interest Calculator to do actual calculations on compound interest.

Interest is the cost of using borrowed money, or more specifically, the amount a lender receives for advancing money to a borrower. When paying interest, the borrower will mostly pay a percentage of the principal (the borrowed amount). The concept of interest can be categorized into simple interest or compound interest.

Simple interest refers to interest earned only on the principal, usually denoted as a specified percentage of the principal. To determine an interest payment, simply multiply principal by the interest rate and the number of periods for which the loan remains active. For example, if one person borrowed $100 from a bank at a simple interest rate of 10% per year for two years, at the end of the two years, the interest would come out to:

$100 × 10% × 2 years = $20

Simple interest is rarely used in the real world. Compound interest is widely used instead. Compound interest is interest earned on both the principal and on the accumulated interest. For example, if one person borrowed $100 from a bank at a compound interest rate of 10% per year for two years, at the end of the first year, the interest would amount to:

$100 × 10% × 1 year = $10

At the end of the first year, the loan's balance is principal plus interest, or $100 + $10, which equals $110. The compound interest of the second year is calculated based on the balance of $110 instead of the principal of $100. Thus, the interest of the second year would come out to:

$110 × 10% × 1 year = $11

The total compound interest after 2 years is $10 + $11 = $21 versus $20 for the simple interest.

Because lenders earn interest on interest, earnings compound over time like an exponentially growing snowball. Therefore, compound interest can financially reward lenders generously over time. The longer the interest compounds for any investment, the greater the growth.

As a simple example, a young man at age 20 invested $1,000 into the stock market at a 10% annual return rate, the S&P 500's average rate of return since the 1920s. At the age of 65, when he retires, the fund will grow to $72,890, or approximately 73 times the initial investment!

While compound interest grows wealth effectively, it can also work against debtholders. This is why one can also describe compound interest as a double-edged sword. Putting off or prolonging outstanding debt can dramatically increase the total interest owed.

Different compounding frequencies

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

The total interest is $5 + $5.25 = $10.25. Therefore, a 10% interest rate compounding semi-annually is equivalent to a 10.25% interest rate compounding annually.

The interest rates of savings accounts and Certificate of Deposits (CD) tend to compound annually. Mortgage loans, home equity loans, and credit card accounts usually compound monthly. Also, an interest rate compounded more frequently tends to appear lower. For this reason, lenders often like to present interest rates compounded monthly instead of annually. For example, a 6% mortgage interest rate amounts to a monthly 0.5% interest rate. However, after compounding monthly, interest totals 6.17% compounded annually.

Our compound interest calculator above accommodates the conversion between daily, bi-weekly, semi-monthly, monthly, quarterly, semi-annual, annual, and continuous (meaning an infinite number of periods) compounding frequencies.

Compound interest formulas

The calculation of compound interest can involve complicated formulas. Our calculator provides a simple solution to address that difficulty. However, those who want a deeper understanding of how the calculations work can refer to the formulas below:

Basic compound interest

The basic formula for compound interest is as follows:

At = A0(1 + r)n

where:

A0 : principal amount, or initial investment
At : amount after time t r : interest rate

n : number of compounding periods, usually expressed in years

In the following example, a depositor opens a $1,000 savings account. It offers a 6% APY compounded once a year for the next two years. Use the equation above to find the total due at maturity:

At = $1,000 × (1 + 6%)2 = $1,123.60

For other compounding frequencies (such as monthly, weekly, or daily), prospective depositors should refer to the formula below.

where:

A0 : principal amount, or initial investment
At : amount after time t n : number of compounding periods in a year r : interest rate

t : number of years

Assume that the $1,000 in the savings account in the previous example includes a rate of 6% interest compounded daily. This amounts to a daily interest rate of:

6% ÷ 365 = 0.0164384%

Using the formula above, depositors can apply that daily interest rate to calculate the following total account value after two years:

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

At = $1,000 × 1.12749

At = $1,127.49

Hence, if a two-year savings account containing $1,000 pays a 6% interest rate compounded daily, it will grow to $1,127.49 at the end of two years.

Continuous compound interest

Continuously compounding interest represents the mathematical limit that compound interest can reach within a specified period. The continuous compound equation is represented by the equation 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 instance, we wanted to find the maximum amount of interest that we could earn on a $1,000 savings account in two years.

Using the equation above:

At = $1,000e(6% × 2)

At = $1,000e0.12

At = $1,127.50

As shown by the examples, the shorter the compounding frequency, the higher the interest earned. However, above a specific compounding frequency, depositors only make marginal gains, particularly on smaller amounts of principal.

Rule of 72

The Rule of 72 is a shortcut to determine how long it will take for a specific amount of money to double given a fixed return rate that compounds annually. One can use it for any investment as long as it involves a fixed rate with compound interest in a reasonable range. Simply divide the number 72 by the annual rate of return to determine 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 grow to $200. Bear in mind that "8" denotes 8%, and users should avoid converting it to decimal form. Hence, one would use "8" and not "0.08" in the calculation. Also, remember that the Rule of 72 is not an accurate calculation. Investors should use it as a quick, rough estimation.

History of Compound Interest

Ancient texts provide evidence that two of the earliest civilizations in human history, the Babylonians and Sumerians, first used compound interest about 4400 years ago. However, their application of compound interest differed significantly from the methods used widely today. In their application, 20% of the principal amount was accumulated until the interest equaled the principal, and they would then add it to the principal.

Historically, rulers regarded simple interest as legal in most cases. However, certain societies did not grant the same legality to compound interest, which they labeled usury. For example, Roman law condemned compound interest, and both Christian and Islamic texts described it as a sin. Nevertheless, lenders have used compound interest since medieval times, and it gained wider use with the creation of compound interest tables in the 1600s.

Another factor that popularized compound interest was Euler's Constant, or "e." Mathematicians define e as the mathematical limit that compound interest can reach.

Jacob Bernoulli discovered e while studying compound interest in 1683. He understood that having more compounding periods within a specified finite period led to faster growth of the principal. It did not matter whether one measured the intervals in years, months, or any other unit of measurement. Each additional period generated higher returns for the lender. Bernoulli also discerned that this sequence eventually approached a limit, e, which describes the relationship between the plateau and the interest rate when compounding.

Leonhard Euler later discovered that the constant equaled approximately 2.71828 and named it e. For this reason, the constant bears Euler's name.

Compound interest (also known as compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. Believed to have originated in 17th-century Italy, compound interest can be thought of as “interest on interest. It will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount.

The rate at which compound interest accrues depends on the frequency of compounding. The higher the number of compounding periods, the greater the compound interest. For example, the amount of compound interest accrued on $100 compounded at 10% annually will be lower than that on $100 compounded at 5% semi-annually over the same time period.

Compound interest has particular importance for young people. The more time you have to take advantage of it, the larger your reward will be down the road. The interest-on-interest mechanism can generate increasingly positive returns based on the initial principal amount, a sort of snowball effect. This has led to the coining of the phrase, “the miracle of compound interest.”

• Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan.
• Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one.
• Interest can be compounded on any given frequency schedule, from continuous to daily to annually.
• When calculating compound interest, the number of compounding periods makes a significant difference.
• The younger you are, the more that compound interest will earn you across your life span. You are in effect supersizing your money.

Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.

The formula for calculating the amount of compound interest is as follows:

• Compound interest = total amount of principal and interest in future (or future value) minus principal amount at present (or present value)

= [P (1 + i)n] – P

= P [(1 + i)n – 1]

Where:

P = principal

i = nominal annual interest rate in percentage terms

n = number of compounding periods

Take a three-year loan of $10,000 at an interest rate of 5% that compounds annually. What would be the amount of interest? In this case, it would be:

$10,000 [(1 + 0.05)3 – 1] = $10,000 [1.157625 – 1] = $1,576.25

Because compound interest includes interest accumulated in previous periods, it grows at an ever-accelerating rate. In the example above, though the total interest payable over the three-year period of this loan is $1,576.25, the interest amount is not the same for all three years, as it would be with simple interest. The interest payable at the end of each year is shown in the table below.

Compound interest can significantly boost investment returns over the long term. While a $100,000 deposit that receives 5% simple annual interest would earn $50,000 in total interest over 10 years, the annual compound interest of 5% on $10,000 would amount to $62,889.46 over the same period. If the compounding period were instead paid monthly over the same 10-year period at 5% compound interest, the total interest would instead grow to $64,700.95.

Interest can be compounded on any given frequency schedule, from daily to annually. There are standard compounding frequency schedules that are usually applied to financial instruments.

The commonly used compounding schedule for savings accounts at banks is daily. For a certificate of deposit (CD), typical compounding frequency schedules are daily, monthly, or semiannually; for money market accounts, it’s often daily. For home mortgage loans, home equity loans, personal business loans, or credit card accounts, the most commonly applied compounding schedule is monthly.

There can also be variations in the time frame in which the accrued interest is actually credited to the existing balance. Interest on an account may be compounded daily but only credited monthly. It is only when the interest is actually credited, or added to the existing balance, that it begins to earn additional interest in the account.

Some banks also offer something called continuously compounding interest, which adds interest to the principal at every possible instant. For practical purposes, it doesn’t accrue that much more than daily compounding interest unless you want to put money in and take it out on the same day.

More frequent compounding of interest is beneficial to the investor or creditor. For a borrower, the opposite is true.

When calculating compound interest, the number of compounding periods makes a significant difference. The basic rule is that the higher the number of compounding periods, the greater the amount of compound interest.

The following table demonstrates the difference that the number of compounding periods can make for a $10,000 loan with an annual 10% interest rate over a 10-year period.

Young people often neglect to save for retirement. For people in their 20s, the future seems so far ahead that other expenses feel more urgent. Yet these are the years when compound interest is a game-changer: Saving small amounts can pay off massively down the road—far more than saving higher amounts later on in life. Here's one example of its effect.

Let’s say you start investing in the market at $100 a month while still in your 20s. Then let’s posit that you average a positive return of 1% a month (12% annually), compounded monthly across 40 years. Now let’s imagine that your twin, who is obviously the same age, doesn’t begin investing until 30 years later. Your tardy sibling invests $1,000 a month for 10 years, averaging the same positive return.

When you hit your 40-year savings mark—and your twin has saved for 10 years—your twin will have generated about $230,000 in savings, while you will have a bit more than $1.17 million. Even though your twin was investing 10 times as much as you (and even more toward the end), the miracle of compound interest makes your portfolio significantly bigger, here by a factor of a little more than five.

The same logic applies to opening an individual retirement account (IRA) and/or taking advantage of an employer-sponsored retirement account, such as a 401(k) or 403(b) plan. Start it in your 20s and be consistent with your payments into it. You’ll be glad you did.

Though the miracle of compounding has led to the apocryphal story of Albert Einstein calling it the eighth wonder of the world or man’s greatest invention, compounding can also work against consumers who have loans that carry very high interest rates, such as credit card debt. A credit card balance of $20,000 carried at an interest rate of 20% compounded monthly would result in a total compound interest of $4,388 over one year or about $365 per month.

On the positive side, compounding can work to your advantage when it comes to your investments and be a potent factor in wealth creation. Exponential growth from compounding interest is also important in mitigating wealth-eroding factors, such as increases in the cost of living, inflation, and reduced purchasing power.

Mutual funds offer one of the easiest ways for investors to reap the benefits of compound interest. Opting to reinvest dividends derived from the mutual fund results in purchasing more shares of the fund. More compound interest accumulates over time and the cycle of purchasing more shares will continue to help the investment in the fund grow in value.

Consider a mutual fund investment opened with an initial $5,000 and an annual addition of $2,400. With an average annual return of 12% over 30 years, the future value of the fund is $798,500. Compound interest is the difference between the cash contributed to an investment and the actual future value of the investment. In this case, by contributing $77,000, or a cumulative contribution of just $200 per month, over 30 years, compound interest is $721,500 of the future balance.

Of course, earnings from compound interest are taxable, unless the money is in a tax-sheltered account. It’s ordinarily taxed at the standard rate associated with your tax bracket and if the investments in the portfolio lose value, your balance can drop.

An investor who opts for a dividend reinvestment plan (DRIP) within a brokerage account is essentially using the power of compounding in whatever they invest.

Investors can also experience compounding interest with the purchase of a zero-coupon bond. Traditional bond issues provide investors with periodic interest payments based on the original terms of the bond issue and because these are paid out to the investor in the form of a check, the interest does not compound.

Zero-coupon bonds do not send interest checks to investors. Instead, this type of bond is purchased at a discount to its original value and grows over time. Zero-coupon-bond issuers use the power of compounding to increase the value of the bond so it reaches its full price at maturity.

Compounding can also work for you when making loan repayments. Making half your mortgage payment twice a month, for example, rather than making the full payment once a month, will end up cutting down your amortization period and saving you a substantial amount of interest.

If it’s been a while since your math class days, fear not: There are handy tools for figuring out compounding. Many calculators (both handheld and computer-based) have exponent functions you can utilize for these purposes.

If more complicated compounding tasks arise, you can perform them in Microsoft Excel in three different ways.

1. The first way to calculate compound interest is to multiply each year’s new balance by the interest rate. Suppose you deposit $1,000 into a savings account with a 5% interest rate that compounds annually, and you want to calculate the balance in five years. In Microsoft Excel, enter “Year” into cell A1 and “Balance” into cell B1. Enter years 0 to 5 into cells A2 through A7. The balance for year 0 is $1,000, so you would enter “1000” into cell B2. Next, enter “=B2*1.05” into cell B3. Then enter “=B3*1.05” into cell B4 and continue to do this until you get to cell B7. In cell B7, the calculation is “=B6*1.05”. Finally, the calculated value in cell B7—$1,276.28—is the balance in your savings account after five years. To find the compound interest value, subtract $1,000 from $1,276.28; this gives you a value of $276.28.
2. The second way to calculate compound interest is to use a fixed formula. The compound interest formula is ((P*(1+i)^n) - P), where P is the principal, i is the annual interest rate, and n is the number of periods. Using the same information above, enter “Principal value” into cell A1 and “1000” into cell B1. Next, enter “Interest rate” into cell A2 and “.05” into cell B2. Enter “Compound periods” into cell A3 and “5” into cell B3. Now you can calculate the compound interest in cell B4 by entering “=(B1*(1+B2)^B3)-B1”, which gives you $276.28.
3. A third way to calculate compound interest is to create a macro function. First start the Visual Basic Editor, which is located in the developer tab. Click the Insert menu, and click on “Module.” Then type “Function Compound_Interest (P As Double, I As Double, N As Double) As Double” in the first line. On the second line, hit the tab key and type in “Compound_Interest = (P*(1+i)^n) - P.” On the third line of the module, enter “End Function.” You have created a function macro to calculate the compound interest rate. Continuing from the same Excel worksheet above, enter “Compound interest” into cell A6 and enter “=Compound_Interest(B1, B2, B3).” This gives you a value of $276.28, which is consistent with the first two values.

A number of free compound interest calculators are offered online, and many handheld calculators can carry out these tasks as well:

• The free compound interest calculator offered through Financial-Calculators.com is simple to operate and offers to compound frequency choices from daily through annually. It includes an option to select continuous compounding and also allows input of actual calendar start and end dates. After inputting the necessary calculation data, the results show interest earned, future value, annual percentage yield (APY) (a measure that includes compounding), and daily interest.
• Investor.gov, a website operated by the U.S. Securities and Exchange Commission (SEC), offers a free online compound interest calculator. It is fairly simple and also allows inputs of monthly additional deposits to the principal, which is helpful for calculating earnings when additional monthly savings are being deposited.
• A free online interest calculator with a few more features is available at TheCalculatorSite.com. This calculator allows calculations for different currencies, the ability to factor in monthly deposits or withdrawals, and the option to have inflation-adjusted increases to monthly deposits or withdrawals automatically calculated as well.

The Truth in Lending Act (TILA) requires that lenders disclose loan terms to potential borrowers, including the total dollar amount of interest to be repaid over the life of the loan and whether interest accrues simply or is compounded.

Another method is to compare a loan’s interest rate to its annual percentage rate (APR), which the TILA also requires lenders to disclose. The APR converts the finance charges of your loan, which include all interest and fees, to a simple interest rate. A substantial difference between the interest rate and APR means one or both of two scenarios: Your loan uses compound interest, or it includes hefty loan fees in addition to interest. Even when it comes to the same type of loan, the APR range can vary wildly among lenders depending on the financial institution’s fees and other costs.

You’ll note that the interest rate you are charged also depends on your credit. Loans offered to those with excellent credit carry significantly lower interest rates than those charged to borrowers with poor credit.

Compound interest simply means that the interest associated with a bank account, loan, or investment increases exponentially—rather than linearly—over time. The key word here is compound.

Suppose you make a $100 investment in a business that pays you a 10% dividend every year. You have the choice of either pocketing those dividend payments like cash or reinvesting them into additional shares. If you choose the second option, reinvesting the dividends and compounding them together with your initial $100 investment, then the returns you generate will start to grow over time.

Compound interest benefits investors, but the meaning of investors can be quite broad. Banks, for instance, benefit from compound interest when they lend money and reinvest the interest they receive into giving out additional loans. Depositors also benefit from compound interest when they receive interest on their bank accounts, bonds, or other investments.

It is important to note that although the term compound interest includes the word interest, the concept applies beyond situations for which the word is typically used, such as bank accounts and loans.

Yes. In fact, compound interest is arguably the most powerful force for generating wealth ever conceived. There are records of merchants, lenders, and various businesspeople using compound interest to become rich for literally thousands of years. In the ancient city of Babylon, for example, clay tablets were used more than 4,000 years ago to instruct students on the mathematics of compound interest. 

In modern times, Warren Buffett became one of the richest people in the world through a business strategy that involved diligently and patiently compounding his investment returns over long periods of time. It is likely that, in one form or another, people will be using compound interest to generate wealth for the foreseeable future.

The long-term effect of compound interest on savings and investments is indeed miraculous. Because it grows your money much faster than simple interest, it is a central factor in increasing wealth. It also mitigates a rising cost of living caused by inflation, as it will almost certainly outpace it.

For young people especially, compound interest is a godsend, as they have the most time ahead of them in which to save. Remember when choosing your investments that the number of compounding periods is just as important as the interest rate. Is there anyone who wouldn’t want to turn $48,000 into $1.17 million, even if it takes 40 years to do it?