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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
- 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.
- 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.
- 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.
- 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}
- 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
- The formula for calculating the value (A) of compound interest is:
- A=P(first+rn)nt{displaystyle A=P(1+{frac {r}{n}})^{nt}}
- 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.
- If compound interest is added annually, we have n=1.
- If compound interest is added quarterly, we have n=4.
- 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} .
- 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}
- 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
- 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}}
- 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.
- 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}
- 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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