# Simple Interest Calculator

Created by Tomasz Jedynak, PhD and Mateusz Mucha
Reviewed by Bogna Szyk and Jack Bowater
Based on research by
Garrett, S. An Introduction to the Mathematics of Finance: A Deterministic Approach 2nd Edition (2013)
Last updated: Jun 05, 2023

Our simple interest calculator calculates monthly payments on an interest-only loan. Just provide the interest percentage and you'll know how much that loan costs.

The difference between "just" interest and mortgage payment is simple - with the mortgage calculator, every month you repay a part of the principal and your loan balance gets lower and lower. With the simple interest calculator, only the interest is paid. The loan amount stays the same forever. Nothing changes with time, so we didn't include a field that would specify your loan's duration.

Simple interest can be used both when you borrow or lend money. In the former case, the interest is added to a separate pile of money each month (and is not subject to extra interest next month).

## What is interest?

The interest is one of the most often used word in finance. Students of the economy become familiar with this term during their very first lectures. Financial advisors, financial officers, stockbrokers, bankers, investment managers, and other financial experts use this term hundreds of times during their everyday activities. So, at the beginning of this article, we will try to answer the question “What is interest?”. Later on, you will find the answers for the following questions:

• What is simple interest?
• What is the difference between simple interest and compound interest?
• What is the formula for simple interest equation and how to find the value of simple interest?
• What are the real-life examples of simple interest loan?

In the next sections, we will also show you some examples of simple interest calculations. But everything in its own time. Let's start with the definition of interest.

Generally, interest is the cost of borrowing money. It is a price that the borrower pays to the lender for using his money. The interest is customarily expressed as a percentage (%) of the original amount (principal amount, balance).

Interest can be either simple or compounded. Simple interest is based on the original amount, while compound interest is based on the original amount and the interest that accumulates on it in every period (for further explanations of simple and compound interest see the section Simple and compound interest).

## Interest rate definition

In finance, interest rate is defined as the amount that is charged by a lender to a borrower for the use of assets. Thus, we can say that for the borrower, the interest rate is the cost of debt, and for the lender, it is the rate of return.

Note here that in case you make a deposit in a bank (e.g., put money in your saving account), from a financial perspective it means that you lend money to the bank. In such a case the interest rate reflects your profit.

The interest rate is commonly expressed as a percentage of the principal amount (loan outstanding or value of deposit). Usually, it is presented on an annual basis. In that case, it is called the annual percentage yield (APY) or the effective annual rate (EAR).

## Simple and compound interest

Simple interest is used to estimate the interest earned or paid on a certain balance (original amount) during a particular period. Simple interest does not take into account the effects of compounding. Compounding means calculating interest on interest. In other words, with compounding you earn the interest not only on the principal amount but also on the interest that was earned over the previous periods. It is essential information, as it means that simple interest may undervalue the amount of interest earned or paid over the considered period.

If you want to assume that interest from the previous periods influence the original amount, you should apply compound interest. Here, we only mention its most basic definition which states that compound interest is the interest calculated on the initial principal and the interest which has been accumulated during the consecutive periods as well.

Note that since simple interest is calculated only on the original amount, it's much easier to determine than compound interest. However, with our calculators, you won't feel the difference.

## Simple interest definition and simple interest formula

According to the widely accepted definition, simple interest is an interest that is paid or computed on the original amount of a loan or the amount of a deposit. The simple interest formula is:

interest = amount * interest_rate

Did you know that the term simple interest was used for the first time in 1798? (That year, the words rentier and working capital appeared in the English language for the first time, too).

## How to calculate simple interest?

Are you wondering how to calculate simple interest? Here is an example that should help you understand it.
Let's assume that you put $1,000 on your savings account. It is the so-called original amount. (Note that you can also treat this $1,000 as the initial value of your loan with simple interest).

• First of all, take the interest rate and divide it by one hundred. 5% = 0.05.
• Then multiply the original amount by the interest rate. $1,000 * 0.05 =$50. That's it. You have just calculated your annual interest!
• To get a monthly interest, divide this value by the number of months in a year (12). $50 / 12 =$4.17. So your monthly interest is $4.17. If the initial $1,000 is a deposit, this is your monthly profit. If this $1,000 is a loan, this value represents your monthly payments. Now let's try to make some further calculations. If you want to compute the sum of the interest paid over a specified period, all you need to do is to multiply the monthly interest by the adequate number of months or years. For example, you may want to calculate the total interest you will receive during next two and a half years. To do so, you need to multiply $4.17 by 30 (2 years = 24 months, half a year = 6 months). $4.17 * 30 =$120.83.

Obviously, all of the above calculations might be done quickly and painlessly with our smart calculator. When testing this tool, don't forget to try the advanced mode.

## An example of simple interest in practice

You inherit $1,000,000 and intend to use it to provide a steady income - you don't want to spend it, nor invest it. You put it into a bank account with a 5% annual interest rate. Every year, you get $50,000 (5% of $1 million). Every month, you'll receive $4,166.67 (1/12 of $50,000). No matter how much time passes, you'll still have$1 million on that account.

## An alternative - compound interest

But what if you were to leave that extra cash on the account? Then that interest would keep working for you and every month the balance on the account would increase (and the whole thing would become an investment. To make it simple, let's assume that the interest compounds annually (is added once per year).

• at the end of the first year, you'd have $1,050,000 ($1 million plus 5%).
• at the end of the second year, you'd have $1,102,500 ($1,050,000 plus 5%).
• 3rd year - $1,157,625. • 10th year - $1,628,894.63.
• 50th year - $11,467,399.79. • 100th year - $131,501,257.85.

Now that's something, isn't it? You wouldn't get your $4,166 every month, but you'd have 131 times more in the bank after 100 years. ## The real-life examples of simple interest loans Well, not everyone will inherit$1,000,000 (although we sincerely wish you that). However, it doesn't mean that you will not come across simple interest in your everyday life. The common examples of use of simple interest are

1. car loans,

2. lines of credit (such as credit cards),

3. discounts on early payments.

4. Assume that you take out a simple interest car loan. If the car costs $5,000 and you don't have any savings, to finance it, you would need to borrow$5,000. It is the principal amount of your car loan. Knowing that the annual interest rate is 3% and the loan must be paid back in one year you can compute the simple interest on that loan as follows:

$5,000 * 3% =$150

In total, you will have to pay back the principal amount plus the interest. So:

$5,000 +$150 = $5,150 1. Assume that you have a credit card with a$2,500 limit and a 15% interest rate that is not compounded*. In the previous month, you bought goods for $1,800, and at the beginning of this month you paid only the minimum amount which was$100. It means that you have a $1,700 balance remaining. The interest that will accrue on your credit card this month is: $1,700 * 15% / 12 = $21.25 However, be aware that credit cards usually have compounded interest rate. Simple interest on credit cards is nowadays rather something extraordinary (Well, try to guess why…) 1. Discounts on early payments are used mainly in business. A seller may offer a discount for his contractor in order to prompt him to pay for the invoice in cash or earlier than its maturity. For example, the issuer of the invoice for$30,000 may offer a 0,2% discount for payment within the week after purchase. It means that the amount of discount is:

$30,000 * 0,2% =$60

So the buyer will have to pay:

$30,000 -$60 = $29,940 Can you calculate the annualized interest rate of this discount? Try to do it by your own and check the result in our easy to use APY calculator. ## Simple interest rate and perpetuity To explain what is perpetuity, we have to start with the term annuity. In the most intuitive sense, an annuity is a series of payments which are made during a specified period at equal intervals. A perpetuity is a specific type of an annuity that has no end. In other words, we could say that perpetuity is a stream of payments that continues forever (indefinitely). Assuming that payments begin at the end of the first period, the monthly payment from perpetuity is calculated with the following formula: monthly payment = principal amount * interest_rate Note, that it is not a coincidence that the above formula is very similar to the simple interest formula presented in the section Simple interest definition and simple interest formula (interest = amount * interest_rate). In fact, we calculate the same value, only the names of the variables have changed. Are you curious what is the value of the principal amount that guarantees you don't have to work anymore? Let's assume that to do so, you need a yearly income equal to$100,000. We also need to assume that, the interest rate is 4% and is constant over time. Thus:

$100,000 = principal amount * 4% So: principal amount =$100,000 / 4% = $2,500,000 Hmm… quite a lot, isn't it? Unfortunately, even if you had such an amount, currently there are only a few existing financial products that are based on the concept of perpetuities. However, in the past, they were issued by many financial institutions (insurers and bank) and even the governments. For example, the so-called consols were issued by the British government and were finally redeemed in 2015. ## Further interest rate calculations Now you know what is simple interest and how to calculate its value. So it's the high time you become familiar with more complex concepts of financial mathematics. Undoubtedly, the term which is the most associated with simple interest is compound interest. We have already described this idea in one of the previous sections. But, did you know that calculations based on compound interest may be used to compute the future value of your investment or savings? All you need to do is use one of our smart calculators. You may also be curious how to compare several bank deposit (or loan) offers if they have different compounding periods and different interest rates. To do so, you need to compute the Annual Percentage Yield, which is also known as the Effective Annual Rate (EAR). This value tells you what is the interest rate on a yearly basis and thus helps you make the best (i.e., the most reasonable) financial decision. However, you can also do it on your own. If you are not sure how to do this, read the APY calculator description where everything is explained in detail. Another fascinating thing you can do when going deeper in interest calculations is to compute how long it would take to increase your investment by n%. Are you curious how much time you need to double your initial investment? Triple it? We suggest you use our smart rule of 72 calculator. ## Interest rate calculators in everyday life If you want to apply the concept of interest rate to everyday life situations, you can try the following tools designed by the Omni team: ## Interest rate in business calculations The concept of interest rate is also widely applied to various business calculations. Here you have a few examples of our business calculators in which the interest rate plays an important role. • The present value calculator estimates the current value of a future payment given a certain rate of return (note that here, the rate of return is the same as the interest rate!). • The NPV calculator gives you the information about the expected profitability of a planned investment project. • The discounted cash flow calculator (DCF) uses the concept of interest rate (here – discount rate) in estimating how much a company is worth. ## FAQ ### What is the difference between simple and compound interest? The difference between simple and compound interest is that simple interest is paid on the initial principal (loan or deposit), while compound interest is calculated using the initial loan or deposit and any earned interest on top of that. ### How do you find the future value of simple interest? To find the future value, F, of simple interest, follow these steps: 1. Write down the simple interest value, r. 2. Write down the present value, P. 3. Set how long in the future, t, you wish to calculate future value for. 4. Replace the parameters in the future value formula F = P × (1 + r × t). ### What is principal in simple interest? The principal, or principal amount, is the initial amount of money lent or invested. The letter P denotes the principal, and it's the value on which interest is calculated. ### What is 6% interest on a$30,000 loan?

6% interest on a $30,000 loan is$1,800 per year or $150 per month. You can quickly calculate simple interest by finding the 6% of 30000: 6 × 30000 / 100 = 1800 Tomasz Jedynak, PhD and Mateusz Mucha Loan amount$
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