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This article was co-written by Andrew Lokenauth. Andrew Lokenauth is a financier with over 15 years of experience working on Wall Street and in startups & technology. Andrew helps management convert financial resources into viable business decisions. He has worked at Gpdman Sachs, Citi and JPMorgan Asset Management. He is the founder of Fluent in Finance – a resource company that helps customers increase their financial resources, understand the importance of investing, make a good budget, plan for repayment, build a vacation schedule. retirement and personal investment planning. Many magazines such as Forbes, TIME, Business Insider, Nasdaq, Yahoo Finance, BankRate and US News have republished his expertise. Andrew holds a bachelor’s degree in Business Administration, Accounting and Finance from Pace University.
This article has been viewed 117,045 times.
Almost everyone knows the concept of interest, but not everyone knows how to calculate interest. Interest is the value added to a loan or deposit to pay interest on one’s use of money over time. Interest can be calculated in 3 basic ways. Simple interest is the easiest calculation, usually applied to short-term loans. Compound interest is calculated slightly more complicated and has a slightly higher value. Finally, continuous compounding is the fastest growing interest rate and is the interest formula most banks use for mortgage loans. The necessary data used in the above calculations are generally the same, but the calculation is slightly different.
Steps
Calculate simple interest
![Image titled Calculate Interest Step 1](https://www.wikihow.com/images_en/thumb/a/ad/Calculate-Interest-Step-1-Version-3.jpg/v4-460px-Calculate-Interest-Step-1-Version-3.jpg)
- In either case, whether you earn interest or pay interest, the amount of capital is usually denoted by the variable P. [1] X Research Source
- For example, if you lend a friend $2,000, your principal will be $2,000.
![Image titled Calculate Interest Step 2](https://www.wikihow.com/images_en/thumb/f/fb/Calculate-Interest-Step-2-Version-3.jpg/v4-460px-Calculate-Interest-Step-2-Version-3.jpg)
- For example, suppose you lend money to a friend with an agreement that the borrower will repay you $2,000 plus interest at 1.5% at the end of the 6th month from the loan date. Before calculating the 1.5% interest rate, you will have to convert 1.5% to a decimal. To convert a percentage to a decimal, divide the number by 100:
- 1.5% ÷ 100 = 0.015.
![Image titled Calculate Interest Step 3](https://www.wikihow.com/images_en/thumb/e/e1/Calculate-Interest-Step-3-Version-3.jpg/v4-460px-Calculate-Interest-Step-3-Version-3.jpg)
- It is important that the loan term must match the interest rate, or at least have the same unit. For example, if interest is charged for one year, the loan term must also be calculated in years. If the interest rate is 3% a year but the loan term is only 6 months, you will charge annual interest with a term of 0.5 years.
- As another example, if the agreed interest rate is 1% per month and you borrow money for 6 months, the loan term will be calculated as 6.
![Image titled Calculate Interest Step 4](https://www.wikihow.com/images_en/thumb/1/18/Calculate-Interest-Step-4-Version-3.jpg/v4-460px-Calculate-Interest-Step-4-Version-3.jpg)
- I=P∗r∗t{displaystyle I=P*r*t}
- Using the example above, the capital you lend to a friend ( P{displaystyle P} ) is $2,000, and the interest rate ( r{displaystyle r} ) is 0.015 for 6 months, variable t{displaystyle t} in this case it is 1. The calculation of interest will be as follows:
- I=Prt=(2000)(0,015)(first)=30{displaystyle I=Prt=(2000)(0.015)(1)=30} . Thus, the interest due will be $30.
- If you want to calculate the total amount due to be received (A), with interest and principal return, we will use the formula A=P(first+rt){displaystyle A=P(1+rt)} . The calculation is expressed as follows:
- A=P(first+rt){displaystyle A=P(1+rt)}
- A=2000(first+0,015∗first){displaystyle A=2000(1+0.015*1)}
- A=2000(first,015){displaystyle A=2000(1,015)}
- A=2030{displaystyle A=2030}
![Image titled Calculate Interest Step 5](https://www.wikihow.com/images_en/thumb/4/49/Calculate-Interest-Step-5-Version-3.jpg/v4-460px-Calculate-Interest-Step-5-Version-3.jpg)
- A=P(first+rt){displaystyle A=P(1+rt)}
- A=5000(first+0,03∗0,25){displaystyle A=5000(1+0.03*0.25)}
- A=5000(first,0075){displaystyle A=5000(1,0075)}
- A=5037,5{displaystyle A=5037.5}
- In 3 months, you will have a profit of $37.50.
- Note, here t=0.25, because 3 months is a quarter (0.25) of the original one-year term.
Calculate compound interest
![Image titled Calculate Interest Step 6](https://www.wikihow.com/images_en/thumb/b/bd/Calculate-Interest-Step-6-Version-3.jpg/v4-460px-Calculate-Interest-Step-6-Version-3.jpg)
- The formula for calculating the value (A) of compound interest is:
- A=P(first+rn)nt{displaystyle A=P(1+{frac {r}{n}})^{nt}}
![Image titled Calculate Interest Step 7](https://www.wikihow.com/images_en/thumb/f/fb/Calculate-Interest-Step-7-Version-3.jpg/v4-460px-Calculate-Interest-Step-7-Version-3.jpg)
![Image titled Calculate Interest Step 8](https://www.wikihow.com/images_en/thumb/2/26/Calculate-Interest-Step-8-Version-3.jpg/v4-460px-Calculate-Interest-Step-8-Version-3.jpg)
- For example, a credit card has an interest rate of 15% a year. However, interest is usually paid on a monthly basis, so you may want to know what the monthly interest rate is. In this case, we would divide the annual interest rate by 12 to get a monthly rate of 1.25%. An interest rate of 15% a year is equivalent to 1.25% a month.
![Image titled Calculate Interest Step 9](https://www.wikihow.com/images_en/thumb/c/c1/Calculate-Interest-Step-9-Version-2.jpg/v4-460px-Calculate-Interest-Step-9-Version-2.jpg)
- If compound interest is added annually, we have n=1.
- If compound interest is added quarterly, we have n=4.
![Image titled Calculate Interest Step 10](https://www.wikihow.com/images_en/thumb/4/45/Calculate-Interest-Step-10-Version-3.jpg/v4-460px-Calculate-Interest-Step-10-Version-3.jpg)
- For example, with a 1-year loan, we have t=first{displaystyle t=1} . However, for a duration of 18 months, we have t=first,5{displaystyle t=1.5} .
![Image titled Calculate Interest Step 11](https://www.wikihow.com/images_en/thumb/0/05/Calculate-Interest-Step-11.jpg/v4-460px-Calculate-Interest-Step-11.jpg)
- First, we will define the variables that you need to solve the calculation. In this field:
- P=$5,000 won{displaystyle P=$5,000}
- r=0,05{displaystyle r=0.05}
- n=twelfth{displaystyle n=12}
- t=3{displaystyle t=3}
![Image titled Calculate Interest Step 12](https://www.wikihow.com/images_en/thumb/e/ef/Calculate-Interest-Step-12.jpg/v4-460px-Calculate-Interest-Step-12.jpg)
- With the above problem, the calculation will be expressed as follows:
- A=P(first+rn)nt{displaystyle A=P(1+{frac {r}{n}})^{nt}}
- A=5000(first+0,05twelfth)twelfth∗3{displaystyle A=5000(1+{frac {0.05}{12}})^{12*3}}
- A=5000(first+0,00417)36{displaystyle A=5000(1+0.00417)^{36}}
- A=5000(first,00417)36{displaystyle A=5000(1,00417)^{36}}
- A=5000(first,1616){displaystyle A=5000(1,1616)}
- A=5808{displaystyle A=5808}
- Thus, after 3 years, the interest will increase by $808, in addition to the original deposit of $5,000.
Calculating compound interest continuously
![Image titled Calculate Interest Step 13](https://www.wikihow.com/images_en/thumb/5/56/Calculate-Interest-Step-13.jpg/v4-460px-Calculate-Interest-Step-13.jpg)
- Using a number of calculations, mathematicians developed a formula based on interest compounded and accrued to an account on a continuous stream. This formula is expressed as follows:
- A=Pert{displaystyle A=Pe^{rt}}
![Image titled Calculate Interest Step 14](https://www.wikihow.com/images_en/thumb/6/66/Calculate-Interest-Step-14.jpg/v4-460px-Calculate-Interest-Step-14.jpg)
- A{displaystyle A} is the future value (or amount) of the loan after interest has been included.
- P{displaystyle P} is the original capital.
- e{displaystyle e} . Although it looks like a variable, it is actually a constant. Alphabet e{displaystyle e} is a special number called the “Eulerian constant,” named after the mathematician Leonard Euler, who discovered its properties.
- Most graphing calculators have a . button ex{displaystyle e^{x}} . If you press this button with the number 1 to indicate efirst{displaystyle e^{1}} , you will find the value of e{displaystyle e} is approximately 2,718.
- r{displaystyle r} is the annual interest rate.
- t{displaystyle t} is the loan term in years.
![Image titled Calculate Interest Step 15](https://www.wikihow.com/images_en/thumb/b/bd/Calculate-Interest-Step-15.jpg/v4-460px-Calculate-Interest-Step-15.jpg)
- P=200,000 yen{displaystyle P=200,000}
- e{displaystyle e} , again, this is not a variable but the constant 2.718.
- r=0,042{displaystyle r=0.042}
- t=30{displaystyle t=30}
![Image titled Calculate Interest Step 16](https://www.wikihow.com/images_en/thumb/9/98/Calculate-Interest-Step-16.jpg/v4-460px-Calculate-Interest-Step-16.jpg)
- A=Pert{displaystyle A=Pe^{rt}}
- A=200000∗2,718(0,042)(30){displaystyle A=200000*2.718^{(0.042)(30)}}
- A=200000∗2,718first,26{displaystyle A=200000*2.718^{1.26}}
- A=200000∗3,525{displaystyle A=200000*3,525}
- A=705000{displaystyle A=705000}
- Note the huge value of continuous compounding.
This article was co-written by Andrew Lokenauth. Andrew Lokenauth is a financier with over 15 years of experience working on Wall Street and in startups & technology. Andrew helps management convert financial resources into viable business decisions. He has worked at Gpdman Sachs, Citi and JPMorgan Asset Management. He is the founder of Fluent in Finance – a resource company that helps customers increase their financial resources, understand the importance of investing, make a good budget, plan for repayment, build a vacation schedule. retirement and personal investment planning. Many magazines such as Forbes, TIME, Business Insider, Nasdaq, Yahoo Finance, BankRate and US News have republished his expertise. Andrew holds a bachelor’s degree in Business Administration, Accounting and Finance from Pace University.
This article has been viewed 117,045 times.
Almost everyone knows the concept of interest, but not everyone knows how to calculate interest. Interest is the value added to a loan or deposit to pay interest on one’s use of money over time. Interest can be calculated in 3 basic ways. Simple interest is the easiest calculation, usually applied to short-term loans. Compound interest is calculated slightly more complicated and has a slightly higher value. Finally, continuous compounding is the fastest growing interest rate and is the interest formula most banks use for mortgage loans. The necessary data used in the above calculations are generally the same, but the calculation is slightly different.
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