Compound Interest Calculator [with formula] (2023)

thiscompound interest calculatoris a tool that can help youEstimate how much you will earn from your deposit.In order to make informed financial decisions, you need to be able to foresee the end result. That's why it's worth knowing how to calculate compound interest. The most common real-life application of the compound interest formula is regular savings calculations.

Read on to find answers to the following questions:

What is the definition of interest rate?
What is the definition of compound interest, and what is the compound interest formula?
What is the difference between simple interest rate and compound interest rate?
How to calculate compound interest?
What is the most common compounding frequency?

interest rate definition

In finance, the interest rate is defined asThe amount charged by the lender to the borrower for the use of the asset.So for the borrower the interest rate is the cost of debt and for the lender it is the rate of return.

Note that where you deposit money with a bank (for example, depositing money into your savings account), from a financial point of view, you have already lent money to the bank. In this case, the interest rate reflects your profit.

Interest rates are usually expressed as a percentage of the principal amount (the outstanding loan or deposit value). Typically, it is presented on an annual basis, known as the Annual Percentage Yield (APY) or Effective Annual Rate (EAR).

What is the definition of compound interest?

Typically, compound interest is defined asEarn interest not only on the initial investment amount but also on any further interest.In other words, compound interest is interest on the initial principalandInterest accrued to date in accordance with this principle. Therefore, the basic characteristic of compound interest isinterest itself earns interest. This concept of increasing book charges allows deposits or loans to grow at a faster rate.

You can use the compound interest equation to calculate the value of an investment after a certain period of time, or to estimate the interest rate you'll earn when buying or selling certain investments. It also lets you answer some other questions, such as how long it will take your investment to double.

We'll answer these questions in the examples below.

Simple and compound interest

You should knowpure interestis different fromcompound interest.It is calculated based on the initial amount only. Compound interest, on the other hand, is the interest on the initial principal plus the interest that has already accrued.

compounding frequency

Most financial advisors will tell you that compounding frequency is the number of compounding periods in a year. But if you're not sure what compounding is, this definition will mean nothing to you... To understand the term, you should know that compounding frequency is the answer to the questionHow often is the interest added to the principal each year?in other words,The compounding frequency is the period of time over which interest is calculated on top of the initial amount.

For example:

Fiscal year (1/year)The compounding frequency of compound interest isone,
quarterly (4 years)The compounding frequency of compound interest isFour,
monthly (12/year)The compounding frequency of compound interest istwelve.

Note that the greater the frequency of compounding, the greater the final balance. However, even if the frequency is abnormally high, the final value will not exceed a certain limit.

Since the main focus of the calculator is the mechanism of compound interest, we have designed a graph where you can visually track the progress of your annual interest balance. If you choose a compounding frequency higher than annual, the graph will show the additional orEarn additional fractional interest compounded annually through higher frequency.So in this way, you can easily observe the true power of compound interest.

compound interest formula

The compound interest formula is an equation that allows you to estimate how much money your savings account will make. It's rather complicated because it takes into account not only the APR and the number of years, but also the number of times the interest is compounded each year.

The annual compound interest calculation formula is as follows:

$\mathrm{FV} = P\cdot\left(1+ \frac r m\right)^{m\cdot t},$ FV=P⋅(1+ricer)rice⋅Ton,

Where:

$\math{FV}$ FV– the future value of the investment, which in our calculator isfinal balance
$P$ P–initial balance(investment value);
$r$ r- annualinterest rate(decimal);
$rice$ rice– the number of times the interest is compounded per year (composite frequency);and
$Ton$ Ton–number of yearsMoney is for investing.

It is worth knowing that when the compounding period is a ( $m = 1$ rice=1), then the interest rate ( $r$ r) is called CAGR (Compound Annual Growth Rate): You can find it in ourCompound Annual Growth Rate Calculator.

(Video) Compound Interest on a Calculator

How to Calculate Compound Interest

In fact, you don't need to memorize the compound interest formula from the previous section to estimate the future value of your investment. In fact, you don't even need to know how to calculate compound interest! Thanks to our compound interest calculator, you can do it in seconds anytime, anywhere.

With our smart calculator you can calculate the future value of your investment simply by filling in the corresponding fields:

main performance

initial balance– The amount you want to invest or deposit.
interest rate– Annual interest rate.
semester– The time frame you want to invest in.
composite frequency– In this field, you should select how often the compound should be applied to your balance. Typically, interest is added to the principal balance on a daily, weekly, monthly, quarterly, semi-annual, or annual basis. But you can also set it up for continuous compounding, which is the theoretical limit to the frequency of compounding. In this case, the number of periods over which compounding occurs is infinite.

additional deposit

How many– The amount you plan to deposit into the account.
frequent– Here you can choose how often you want to make additional deposits.
when– You should choose the trading hours for additional deposits. More specifically, you can deposit money into an accountat firstorat the endperiod.
deposit growth rate– This option allows you to set the growth rate for additional deposits. This option can be especially useful in the long run when your earnings are likely to increase due to factors such as inflation and/or promotions.

That's it! In an instant, our compound interest calculator does all the necessary calculations for you and gives you the results.

The two main results are:

compound interest example

Do you want to understand the compound interest equation?
Are you curious about the details of how compound interest is calculated?
Do you want to know how our calculator works?
Do you need to know how to interpret the results of compound interest calculations?
Are you interested in all possible uses of the compound interest formula?

The following examples are intended to try to help you answer these questions. We are confident that after learning them, you will have no difficulty understanding and actually implementing compound interest.

Example 1 - Basic calculation of investment value

The first example is the simplest, where we calculate the future value of the initial investment.

question

You invest $10,000 at 5% annual interest for 10 years. The interest rate is compounded annually. What is your investment worth in 10 years?

solution

First let's determine what value is given and what value we need to find. we know you want to invest $\$10000$ $10000– This is your initial balance $P$ P, the number of years you want to invest is $10$ 10.In addition, interest rates $r$ requal $5\%$ 5%, the interest is compounded annually, so $rice$ ricein the compound interest formula is equal to $1$ 1.

We want to calculate the amount you will get from this investment. That is, we require the future value $\math{FV}$ FVyour investment.

To calculate it, we need to plug the appropriate numbers into the compound interest formula:

$\begin{split}\mathrm{FV}& = 10,\!000 \cdot \left(1 + \frac{0.05}{1}\right) ^ {10\cdot1} \\&= 10,\!000 \cdot 1.628895 \\&= 16,288.95\end{split}$ FV=10,000⋅(1+10.05)10⋅1=10,000⋅1.628895=16,288.95

answer

After 10 years your investment will be worth $16,288.95.

your profit will be $\mathrm{FV} - P$ FV−P.This is $\$16288.95 - \$10000.00 = \$6288.95$ $16288.95−$10000.00=$6288.95.

Note that you have to be very careful with rounding when doing calculations. You shouldn't do much until the end. Otherwise, your answer may be incorrect. Accuracy depends on the values you calculate. For standard calculations, six decimal places are sufficient.

Example 2 - Complex calculation of investment value

In the second example, we calculate the future value of an initial investment compounded monthly.

question

You invest $10,000 at 5% annual interest. The interest rate is compounded monthly. What is your investment worth in 10 years?

solution

As with the first example, we should determine the value first. initial balance $P$ Pyes $\$10000$ $10000, the number of years you want to invest is $10$ 10, interest rate $r$ requal $5\%$ 5%, and the compounding frequency $rice$ riceyes $12$ 12.We need to get the future value $\math{FV}$ FVinvestment.

Let's plug in the appropriate numbers in the compound interest formula:

(Video) Compound Interest Formula

$\begin{split}\mathrm{FV}& = 10,\!000 \cdot\left(1 + \frac{0.05}{12}\right) ^ {10\cdot12}\\[1em]& = 10, \!000 \cdot 1.004167 ^ {120}\\& = 10,\!000 \cdot 1.647009 \\&= 16,470.09\end{split}$ FV=10,000⋅(1+120.05)10⋅12=10,000⋅1.004167120=10,000⋅1.647009=16,470.09

answer

In 10 years your investment will be worth $\$16470.09$ $16470.09.

your profit will be $\mathrm{FV} - P$ FV−P.This is $\$16470.09 - \$10000.00 = \$6470.09$ $16470.09−$10000.00=$6470.09.

Did you notice that this example is very similar to the first one? In fact, the only difference is the composite frequency. Note that just because of the more frequent compounding this time around, you will get $\$181.14$ $181.14More in the same period: $\$6470.09 - \$6288.95 = \$181.14$ $6470.09−$6288.95=$181.14.

Example 3 - Calculate investment interest rate using compound interest formula

Now, let's try different types of questions that can be answered using the compound interest formula. This time, some basic algebraic transformations will be required. In this example we will consider a situation where we know the initial balance, final balance, number of years and compounding frequency, but require us to calculate the interest rate. This type of calculation might be useful if you want to determine the interest rate you earn when buying or selling assets (for example, property) that you use as investments.

Data and Questions
You paid $2,000 for an original painting. Six years later, you sell the painting for $3,000. Assuming the painting is considered an investment, what is your annual income?

solution
First, let's determine the given values. initial balance $P$ Pyes $\$2000$ $2000and final balance $\math{FV}$ FVyes $\$3000$ $3000.The investment time frame is $6$ 6year, the calculation frequency is $1$ 1.This time, we need to calculate the interest rate $r$ r.

Let's try plugging these numbers into a basic compound interest formula:

$3,\!000 = 2,\!000 \cdot\left(1 + \frac r 1\right) ^{6\cdot1}$ 3,000=2,000⋅(1+1r)6⋅1

so:

$3,\!000 = 2,\!000 \cdot(1 + r) ^6$ 3,000=2,000⋅(1+r)6

We can solve this equation using the following steps:
Divide both sides by $2000$ 2000:

$\frac{3,\!000}{2,\!000}= (1 + r) ^ 6$ 2,0003,000=(1+r)6

Raise the sides to 1/6^Daystrength:

$\frac{3,\!000}{2,\!000}^ {\frac 1 6} = (1 + r)$ 2,0003,00061=(1+r)

minus $1$ 1From both sides:

$\frac{3,\!000}{2,\!000} ^{\frac 1 6} – 1 = r$ 2,0003,00061–1=r

finally resolved to $r$ r:

$\begin{split}r & = 1.5 ^ {0.166667 }– 1\\& = 1.069913 - 1 \\&= 0.069913 = 6.9913\%\end{split}$ r=1.50.166667–1=1.069913−1=0.069913=6.9913%

answer

In this example, you made $1,000 over six years from an initial investment of $2,000, which means your annual interest rate equals 6.9913%.

This time you can see that the formula is not very simple and requires a lot of calculations. That's why it's worth testing our compound interest calculator, which solves the same equation in no time, saving you time and effort.

(Video) Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra

Example 4 - Calculate the doubling time of an investment using the compound interest formula

Have you ever wondered how many years it takes for your investment to double in value? Among other things, our calculator can help you answer this question. To see how it does it, let's look at the example below.

Data and Questions

You deposit $1,000 into your savings account. Assume that the interest rate equals 4% and is compounded annually. Find the number of years after the initial balance doubles.

solution

The given values are as follows: Initial Balance $P$ Pyes $\$1000$ 1,000and final balance $\math{FV}$ FVyes $2 \cdot \$1000 = \$2000$ 2⋅1,000=$2000, and the interest rate $r$ ryes $4\%$ 4%.The calculation frequency is $1$ 1.Time span of investment $Ton$ Tonunknown.

Let's start with the basic compound interest equation:

$\mathrm{FV} = P\cdot \left(1 + \frac{r}{m}\right)^{mt}$ FV=P⋅(1+ricer)riceTon

Know $m = 1$ rice=1, $r = 4\%$ r=4%, and $\mathrm{FV} = 2 \cdot P$ FV=2⋅PWe can write:

$2P = P \cdot(1 + 0.04) ^ t$ 2P=P⋅(1+0.04)Ton

can be written as:

$2P = P\cdot (1.04) ^ t$ 2P=P⋅(1.04)Ton

Divide both sides by $P$ P( $P$ PDefinitely Not $0$ 0！）：

$2 = 1.04 ^ t$ 2=1.04Ton

solve $Ton$ Ton, you need to take the natural logarithm ( $\ln$ exist), both parties:

$\ln(2) = t \cdot \ln(1.04)$ exist(2)=Ton⋅exist(1.04)

so:

$t\!=\! \frac{\ln(2)}{\ln(1.04) }\!=\! \frac{0.693147}{0.039221 }\!= \! 17.67$ Ton=exist(1.04)exist(2)=0.0392210.693147=17.67

answer

In our example, it would take 18 years (18 being the nearest integer greater than 17.67) to double the initial investment.

Did you notice that in the above solution, we don't even need to know the initial and final balance of the investment? This is thanks to the simplification we made in the third step (Divide both sides by $P$ P). However, you will need to provide this information in the appropriate field when using our compound interest calculator. If you just want to find out when a given interest rate will double your investment, don't worry; just enter any number (for example, $1$ 1and $2$ 2).

It's also worth mentioning that the exact same calculation can be used to figure out when an investment will triple (or multiply by any number, in fact). All you need to do is use different multiples of P in the second step of the above example. You can also use our calculator to calculate.

compound interest table

Before the days of calculators, PCs, spreadsheets and the incredible solutions provided by the Omni Calculator, compound interest tables were used every day 😂. These tables are designed to make financial calculations easier and faster (yes, really...). They are included as appendices in many older finance textbooks.

(Video) Compound Interest - Easy Example + Practice

Below, you can see what a compound interest table looks like.

Compound Interest Calculator [with formula] (1)

Using the data provided in the compound interest table, you can calculate the final balance of your investment. You just need to know the columncompound quantity factorshow the value of the factor $(1 + r)^t$ (1+r)Tonfor the respective interest rates (first row) and t (first column). Therefore, to calculate the final balance of an investment, you need to multiply the initial balance by the appropriate value from the table.

Note that the values in the columnpresent value coefficientUsed to calculate the present value of an investment when you know its future value.

Obviously, this is just a basic example of a compound interest table. In fact, they are usually much larger because they contain more cycles $Ton$ Tonvarious interest rates $r$ rand different composite frequencies $rice$ rice...you have to scroll through dozens of pages to find the proper value for the compound amount factor or the present value factor.

With new knowledge of the world of financial computing ahead of Omni Calculator, do you like our tool? Why not share it with your friends? Let them know about Omni! If you want to be financially savvy, you can also try our other financial calculators.

Additional Information

Now that you know how to calculate compound interest, it's time to find other apps to help you get the most out of your investments:

To compare bank quotes with different compounding periods, we need to calculate the annual rate of return, also known as the effective annual rate (EAR). This value tells us how much profit we will make in a year. The most comfortable way to figure it out is to useyear calculator, which estimates the EAR based on the interest rate and compounding frequency.

If you want to know how long it takes for something to increase by n%, you can use ourRule of 72 Calculator.This tool allows you to check how long it will take you to double your investment faster than a compound interest calculator.

You may also be interested in the following contentCredit Card Earnings Calculator, which allows you to estimate how long it will take to be completely debt-free.

thisdepreciation calculatorEnables you to estimate how quickly your property's value will decline over time using three different methods.

FAQ

What is compound interest?

Compound interest is a type of interest calculated on an initial balance and accrued interest over previous periods. Basically you can think of it asearn interest.

What is the difference between simple interest and compound interest?

While simple interest only earns interestinitial balance, compound interest on the initial balance andAccumulated interest in previous period.

How do I calculate compound interest?

To calculate compound interest, you must usecompound interest formula, which will displayFVFuture value of investment (or future balance):

FV = P × (1 + (r / m))^{(m x ton)}

The formula takes into account the initial balanceP, the annual interest rater, composite frequencyrice, and the number of yearsTon.

How long does it take for $1,000 to double?

To use compound interest rates, you need17 years and 8 monthsDoubling (accounting for annual compounding frequency and 4% interest rate). To calculate this:

Use the compound interest formula:
FV = P × (1 + (r / m))^{(m x ton)}
replacement value.future valueFVtwice the initial balanceP, interest rater = 4%, and frequencym = 1:
2P = P × (1 + (0.04 / 1))^{(1 × t)}
2 = (1.04)^Ton
solvetimeTon:
(Video) Compound Interest
t = ln(2) / ln(1.04)
t = 17.67 years = 17 years and 8 months

FAQs

What is the formula to calculator compound interest? ›

Compound interest, can be calculated using the formula FV = P*(1+R/N)^(N*T), where FV is the future value of the loan or investment, P is the initial principal amount, R is the annual interest rate, N represents the number of times interest is compounded per year, and T represents time in years.

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How much is $1000 worth at the end of 2 years if the interest rate of 6% is compounded daily? ›

Compound interest formulas

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.

What is the easiest formula for compound interest? ›

Formula of Compound Interest

Hence, the formula to find just the compound interest is as follows: CI = P (1 + r/n)^nt - P. In the above expression, P is the principal amount. r is the rate of interest(decimal obtained by dividing rate by 100)

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How much would $10000 on deposit at a five percent annual simple interest rate for three years earn? ›

Thus, if simple interest is charged at 5% on a $10,000 loan that is taken out for three years, then the total amount of interest payable by the borrower is calculated as $10,000 x 0.05 x 3 = $1,500.

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What are the three steps to calculating compound interest? ›

To determine the CAGR of an investment, you can follow three simple steps:

Divide the value of an investment after a compounding period by its value at the start of that period.
Raise the result to an exponent of one divided by the number of years.
Subtract one from the result.

Jun 24, 2022

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What is the formula for compound interest and questions? ›

Compound Interest Formula

The formula for compound interest is A=P(1+rn)nt, where A represents the final balance after the interest has been calculated for the time, t, in years, on a principal amount, P, at an annual interest rate, r. ...
To find the balance after two years, A, we need to use the formula, A=P(1+rn)nt.

More items...

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What is the formula for monthly compound interest? ›

How do you compound interest monthly? CI = P(1 + (r/12) )12t – P is the formula of monthly compound interest where P is the principal amount, r is the interest rate in decimal form, and t is the time.

What is the future value of $1000 a year for five years at a 6% rate of interest? ›

Example 1: Calculate Future Value Using Simple Annual Interest. What is the future value of $1,000 invested today in 5 years assuming 6% simple annual interest rate? The future value will be calculated using the future value formula using simple interest rate and will equal: $1,000 * (1+(0.06*5)), or $1,300.

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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.

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How much interest does 1 million dollars earn in 10 years? ›

Bank Savings Accounts

As noted above, the average rate on savings accounts as of February 3^rd 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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How much interest would 10 million dollars earn in a year? ›

You can find interest rates near the national average of 0.26% or rates as high as 2.25%. With a $10 million portfolio, you'd receive an annual income of $2,600 to $225,000.

What 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.

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What is the number one rule of compounding? ›

Charlie Munger once said that the first rule of compounding is to never interrupt it unnecessarily.

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What is the magic number for compound interest? ›

The magic number

The premise of the rule revolves around either dividing 72 by the interest rate your investment will receive, or inversely, dividing the number of years you would like to double your money in by 72 to give you the required rate of return.

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What will 100 become after 20 years at 5% compound interest? ›

Therefore, the final amount after 20 years at 5% p.a. compound interest on Rs. 100 is Rs. 265.33.

Is a 7% return realistic? ›

According to conventional wisdom, an annual ROI of approximately 7% or greater is considered a good ROI for an investment in stocks. This is also about the average annual return of the S&P 500, accounting for inflation. Because this is an average, some years your return may be higher; some years they may be lower.

How to flip 10K? ›

The Best Ways to Invest 10K

Real estate investing. One of the more secure options is investing in real estate. ...
Product and website flipping. ...
Invest in index funds. ...
Invest in mutual funds or EFTs. ...
Invest in dividend stocks. ...
Peer-to-peer lending (P2P) ...
Invest in cryptocurrencies. ...
Buy an established business.

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How much will I have in 8 years if I invest $10000 at 5% compounded monthly? ›

he amount obtained above is closest to $15,000. Therefore, The total amount accrued, principal plus interest, with compound interest on a principal of $10,000.00 at a rate of 5 percent per year compounded 12 times per year over 8 years is around $15,000.

How long will it take $4000 to double itself if it is invested at 8% simple interest? ›

time=12. 5years.

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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 is the secret formula for compound interest? ›

We need to understand the compound interest formula: A = P(1 + r/n)^nt. A stands for the amount of money that has accumulated. P is the principal; that's the amount you start with. The r is the interest rate.

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How do you calculate compound interest annually with examples? ›

A = P (1 + r / m) ^mt

r (rate of return) = 10% compounded annually. m (number of the times compounded annually) = 1. t (number of years for which investment is made) = three years.

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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.

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How many years will it take to double $100 at an interest rate of 10%? ›

If you had $100 with a 10 percent simple interest rate with no compounding, you'd divide 1 by 0.1, yielding a doubling rate of 10 years. For continuous compounding interest, you'll get more accurate results by using 69.3 instead of 72.

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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%.

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What is the fastest way to calculate compound interest? ›

You can calculate compound interest with a simple formula. It is calculated by multiplying the first principal amount by one and adding the annual interest rate raised to the number of compound periods subtract one. The total initial amount of your loan is then subtracted from the resulting value.

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What are the 4 components of the formula for compound interest? ›

The following are the four main components of compound interest:

Principal. The principal is the amount that is originally deposited in a compounding environment (for example, a high-interest savings account at a bank). ...
Interest rate. ...
Compounding Frequency. ...
Time horizon.

Mar 1, 2020

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What is the formula for annual interest rate? ›

How do you calculate interest per year? The equation for calculating interest rates is as follows: Interest = P x R x N. Where P equals the principal amount (the beginning balance), and R stands for the interest rate (usually per year, expressed as a decimal).

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What is the formula annual interest rate to monthly? ›

To convert annual rate to monthly rate, when using APR, simply divide the annual percent rate by 12.

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