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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.
What is 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.
| At = A0 × (1 + |
| )nt |
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.
FAQs
How much will $1000 saved at 5% interest for 5 years grow to? ›
In 5 years, you'll have $11,000.
How much will $10,000 be worth in 20 years? ›With that, you could expect your $10,000 investment to grow to $34,000 in 20 years.
How long will it take $10000 to double if it is invested at 6% interest compounded continuously? ›This means that the investment will take about 12 years to double with a 6% fixed annual interest rate.
How much is 1000 worth at the end of 2 years if the interest rate of 6% is compounded daily? ›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.
Is it possible to save $100,000 in 5 years? ›If you can afford to put away $1,400 per month, you could potentially save your first $100k in just 5 years. If that's too much, aim for even half that (or whatever you can). Thanks to compound interest, just $700 per month could become $100k in 9 years.
Is it possible to save 1 million dollars in 5 years? ›The number might seem impossible, but you can accomplish it. To save $1 million in five years, you will have to calculate how much you will need to save and which investments can help you reach that goal. Use the tips below to start your journey toward $1 million.
How long to save $1 million in 10 years? ›In order to hit your goal of $1 million in 10 years, SmartAsset's savings calculator estimates that you would need to save around $7,900 per month. This is if you're just putting your money into a high-yield savings account with an average annual percentage yield (APY) of 1.10%.
How much is $100 at 10% interest at the end of each year forever worth today? ›Present value of perpetuity:
So, a $100 at the end of each year forever is worth $1,000 in today's terms.
Bank Savings Accounts
As noted above, the average rate on savings accounts as of February 3rd 2021, is 0.05% APY. A million-dollar deposit with that APY would generate $500 of interest after one year ($1,000,000 X 0.0005 = $500). If left to compound monthly for 10 years, it would generate $5,011.27.
It will take a bit over 10 years to double your money at 7% APR. So 72 / 7 = 10.29 years to double the investment.
How long will it take $4000 to double itself if it is invested at 8% simple interest? ›
time=12. 5years.
How much would $200 invested at 6 interest compounded annually be worth after 6 years? ›Hence, it is worth $283.70, when $200 is invested at 6% interest compounded annually, after 6 years.
What is the future value of $100 invested at 10% simple interest for 2 years? ›Answer: If the Interest Rate is 10 Percent, then the Future Value in Two Years of $100 Today is $120.
How much interest does $100000 earn in a year? ›How much interest can $100,000 earn in a year? If you put $100,000 in CDs, high-yield savings or a money market account for a year, you could earn anywhere from $3,000 to $5,000 based on current interest rates.
How much interest will $200 000 earn in a year? ›Below is how much interest you could earn on $200,000 on an annual basis, from 1% all the way up to a 10% interest rate: $200,000 x 0.01= $2,000. $200,000 x 0.02= $4,000. $200,000 x 0.03= $6,000.
How to invest $100 000 to make $1 million? ›Invest $400 per month for 20 years
If you're earning a 10% average annual return and investing $400 per month, you'd be able to go from $100,000 to $1 million in savings in just over 20 years. Again, if your actual average returns are higher or lower than 10% per year, that will affect your timeline.
| Account balance | Cumulative amount invested | |
|---|---|---|
| After two years | $354,549 | $315,660 |
| After three years | $553,370 | $473,490 |
| After four years | $768,096 | $631,320 |
| After five years | $1,000,000 | $789,150 |
That's pretty good, considering that by age 30, you should aim to have the equivalent of your annual salary saved. The median earnings for Americans between 25 and 34 years old is $40,352, meaning the 16 percent with $100,000 in savings are well ahead of schedule. How much should you have stashed away at other ages?
Can I retire on $2 million at 65? ›Yes, for some people, $2 million should be more than enough to retire. For others, $2 million may not even scratch the surface. The answer depends on your personal situation and there are lot of challenges you'll face. As of 2023, it seems the number of obstacles to a successful retirement continues to grow.
How many Americans have $5 million in savings? ›How many $4 or $5 millionaires are there in the US? Somewhere around 4,473,836 households have $4 million or more in wealth, while around 3,592,054 have at least $5 million. Respectively, that is 3.48% and 2.79% of all households in America.
At what age can you retire with $1 million dollars? ›
$1 million doesn't go nearly as far in retirement as it once did. In fact, a recent survey found that investors believe they'll need at least $3 million to retire comfortably. But retiring with $1 million is still possible, even as early as age 55, if you're smart about it.
Will $10 million dollars last a lifetime? ›Simply put, most people should have no problem retiring at 30 with $10 million. If you invest your money and earn a modest return, $10 million should be enough to retire and never have to work again. Of course, that doesn't mean that running out of money would be impossible.
How many people have $3,000,000 in savings? ›1,821,745 Households in the United States Have Investment Portfolios Worth $3,000,000 or More.
Can 2 million dollars last a lifetime? ›A retirement account with $2 million should be enough to make most people comfortable. With an average income, you can expect it to last 35 years or more.
What is 6% interest on $10000 for 5 years? ›An investment of $10000 today invested at 6% for five years at simple interest will be $13,000.
What is the future value of $100 invested at 10 simple interest for 1 year? ›How much will there be in one year? The answer is $110 (FV). This $110 is equal to the original principal of $100 plus $10 in interest. $110 is the future value of $100 invested for one year at 10%, meaning that $100 today is worth $110 in one year, given that the interest rate is 10%.
How long in years will it take $50000 placed in a savings account at 10% interest to grow into $75000? ›Hence, the time will be 4.25 years.
Am I rich if I have $10 million dollars? ›You might need $5 million to $10 million to qualify as having a very high net worth while it may take $30 million or more to be considered ultra-high net worth. That's how financial advisors typically view wealth.
Where do millionaires keep their money? ›Millionaires have many different investment philosophies. These can include investing in real estate, stock, commodities and hedge funds, among other types of financial investments. Generally, many seek to mitigate risk and therefore prefer diversified investment portfolios.
How many people have $1000000 in savings? ›In fact, statistically, around 10% of retirees have $1 million or more in savings.
What is the rule of 69? ›
The Rule of 69 is used to estimate the amount of time it will take for an investment to double, assuming continuously compounded interest. The calculation is to divide 69 by the rate of return for an investment and then add 0.35 to the result.
What is the rule of 42 in investing? ›The so-called Rule of 42 is one example of a philosophy that focuses on a large distribution of holdings, calling for a portfolio to include at least 42 choices while owning only a small amount of most of those choices.
What is Rule 72 in finance? ›Do you know the Rule of 72? It's an easy way to calculate just how long it's going to take for your money to double. Just take the number 72 and divide it by the interest rate you hope to earn. That number gives you the approximate number of years it will take for your investment to double.
How much would $150 invested at 8 after 17 years? ›A sum of money (i.e. Principal) is $\$ 150$ which is invested at compounded interest (which means we have to use the above formula) at $8\% $ per annum for 17 years. Hence, if $\$ 150$ is invested at $8\% $ interest compounded continuously then its worth after 17 years will be $ \$ 555 $.
How long will it take 1000 dollars to double if it is invested at 6% interest compounded semi annually? ›The answer is: 12 years.
What ROI would I need if I need to double my money in 8 years? ›For example, with a 9% rate of return, the simple calculation returns a time to double of eight years.
How much is $1000 worth at the end of 2 years if the interest rate of 6% is compounded daily? ›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.
How much would $120 invested at 6 after 21 years? ›Binayaka C. Investment of $120.00 will yield $421.72 after 21 years.
What would the future value of $100 be after 5 years at 10% compound interest? ›Answer and Explanation: The $100 investment becomes $161.05 after 5 years at 10% compound interest.
Can I live off interest on a million dollars? ›Once you have $1 million in assets, you can look seriously at living entirely off the returns of a portfolio. After all, the S&P 500 alone averages 10% returns per year. Setting aside taxes and down-year investment portfolio management, a $1 million index fund could provide $100,000 annually.
How much will you have in 10 years if you invest $10000 today at 10% interest? ›
If you invest $10,000 today at 10% interest, how much will you have in 10 years? Summary: The future value of the investment of $10000 after 10 years at 10% will be $ 25940.
How much interest will 1 million dollars earn? ›Bank Savings Accounts
As noted above, the average rate on savings accounts as of February 3rd 2021, is 0.05% APY. A million-dollar deposit with that APY would generate $500 of interest after one year ($1,000,000 X 0.0005 = $500). If left to compound monthly for 10 years, it would generate $5,011.27.
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At $200,000 per year in average returns, this is more than enough for all but the highest spenders to live comfortably. You can collect your returns, pay your capital gains taxes and have plenty left over for a comfortable lifestyle. The bad news about an index fund is the variability.
Can you live off 10 million dollars interest? ›It's entirely possible to live off the interest earned by a $10 million portfolio, depending on how much you need and what your investment choices are. You'll want to make sure that your lifestyle goals are in line with the income produced if you're going to make it through retirement without running out of funds.
How much interest does $3 million dollars earn per year? ›A typical stock dividend portfolio will earn between 2% and 5% in dividends each year. Additionally, the portfolio may grow over time to provide higher dividends and capital gains in the future. On a $3 million portfolio, you can expect to receive $60,000 to $150,000 per year. Real estate investment trust (REIT).
How much interest will I earn with 10 million dollars? ›On average, dividend stock investors earn between 2% to 5% in dividends each year. So, with a $10 million portfolio, you would earn between $200,000 to $500,000 per year.
How long will it take $1000 to double at 5% interest? ›Answer and Explanation: The answer is: 12 years.
What is the future value of $1000 after 5 years at 8 per year? ›An investment of $1,000 made today will be worth $1,480.24 in five years at interest rate of 8% compounded semi-annually.
What would $10,000 become in 5 years at 6 interest? ›An investment of $10000 today invested at 6% for five years at simple interest will be $13,000.
What's the future value of $1000 invested at 10% for five years? ›
Using the above example, the same $1,000 invested for five years in a savings account with a 10% compounding interest rate would have an FV of $1,000 × [(1 + 0.10)5], or $1,610.51.
How many years will it take a $5000 investment to reach $7500 at an 8% interest rate? ›Therefore, it takes 5.17 years for $ 5 , 000 \$5,000 $5,000 to grow to $ 7 , 500 \$7,500 $7,500 if it is invested at 8% compounded semiannually.
What is the 7 year rule in investing? ›Assuming long-term market returns stay more or less the same, the Rule of 72 tells us that you should be able to double your money every 7.2 years. So, after 7.2 years have passed, you'll have $200,000; after 14.4 years, $400,000; after 21.6 years, $800,000; and after 28.8 years, $1.6 million.
How much will $100 K be worth in 20 years? ›How much will $100k be worth in 20 years? If you invest $100,000 at an annual interest rate of 6%, at the end of 20 years, your initial investment will amount to a total of $320,714, putting your interest earned over the two decades at $220,714.
How much is $100 received at the end of each year forever at 10 interest worth today? ›Present value of perpetuity:
So, a $100 at the end of each year forever is worth $1,000 in today's terms.
Bank Savings Accounts
As noted above, the average rate on savings accounts as of February 3rd 2021, is 0.05% APY. A million-dollar deposit with that APY would generate $500 of interest after one year ($1,000,000 X 0.0005 = $500). If left to compound monthly for 10 years, it would generate $5,011.27.
Answer: If the Interest Rate is 10 Percent, then the Future Value in Two Years of $100 Today is $120.
What will $5,000 be worth in 20 years? ›Answer and Explanation: The calculated present worth of $5,000 due in 20 years is $1,884.45.
How much do I need to invest to be a millionaire in 10 years? ›“Say you're going to average 10% a year on your investment return — you're going to need to save about $5,000 each month to save $1 million.” Moore recommends putting this money into an employer-sponsored retirement savings account if possible.
How much will I have if I invest $500 a month for 10 years? ›If you invested $500 a month for 10 years and earned a 4% rate of return, you'd have $73,625 today. If you invested $500 a month for 10 years and earned a 6% rate of return, you'd have $81,940 today.
How much would $10,000 invested in 2000 be worth today? ›
Invest a larger amount — say, $10,000 — and it will really start to snowball: $10,000 invested in 2000 could be worth around $38,000 today.