Calculate Simple Interest

Whenever money is lent from one party to another, the loan will have an interest rate. This interest is the amount of money that must eventually be paid back to the lender, in addition to the original amount lent (known as the principal). When dealing with simple interest, the amount that the borrower is responsible for is calculated by this original principal (denoted by the variable P) being multiplied by the interest rate (denoted by r, for rate), and then multiplied by the period of time that the principal earns interest (denoted by t). Altogether, the equation for calculating simple interest is <math>I=Prt.</math>[1]

Steps

Calculating Simple Interest

  1. Find interest owed with formula <math>I = Prt</math>.
    • <math>I =</math> Interest owed
    • <math>P =</math> Principal, or the initial sum borrowed
    • <math>r =</math> Interest rate written as a decimal
    • <math>t =</math> Number of time periods since loan began
  2. Find total amount owed. The borrower also has to pay back initial loan, so total amount owed is equal to <math>I + P</math>. You can either add them together at the end, or combine them into one equation to get total amount <math>A = P(1 + rt)</math>.
  3. Example A. A bank lends you $55,000 at a simple annual interest rate of 3%. How much interest do you owe ten years later?
    • <math>P = $55,000</math>
    • <math>r = 0.03 / \text{year}</math> (To convert a percentage to a decimal, divide by 100. For example, if you're given a rate of 3%, it becomes 3/100, or 0.03)
    • <math>t = 10 \ \text{years}</math>
    • <math>I = Prt = ($55,000)(0.03/ \text{year})(10 \ \text{years}) = $16,500</math>
    • <math> \text{Total amount owed} = $55,000 + $16,500 = $71,500 </math>
  4. Example B. Your friend borrows $70 and agrees to pay 5% simple interest every week. Two months later, how much does your friend owe?
    • <math>P = $70</math>
    • <math>r = 0.05/ \ \text{week}</math>
    • <math>t = 2 \ \text{months} \times (4 \ \text{weeks}/ \text{month}) = 8 \ \text{weeks}</math> (Interest is calculated per week in this problem, so we must count t in terms of weeks.)
    • <math>I = Prt = ($70)(0.05/ \text{week})(8 \ \text{weeks}) = $28</math>
    • <math>\text{Total amount owed} = I + P = $28 + $70 = $98</math>

Understanding Concepts

  1. Understand interest. Why does interest exist? The person lending money is giving up other uses for that money until the loan is repaid. The interest is supposed to make up for the fact that the lender could have spent that money in ways the brought in extra value.[2]
  2. Pay attention to the time period for each loan. Interest accumulates over regularly-spaced periods of time. For annual interest the time periods are years, but the terms of the loan could use months, weeks, or days. The shorter the period of time, the more often interest gets added to the loan.
    • This can make a huge difference. A loan with annual interest adds the interest rate ten times in ten years. A loan with monthly interest adds the same interest rate 120 times in ten years:
      • <math>10 \ \text{years} \times \frac{12 \ \text{months}}{1 \ \text{year}} = 120</math>
  3. Don't forget the principal. When a loan is paid off, the borrower doesn't only have to pay the interest — they must also pay back the principal that was borrowed. The sum of the interest generated plus the principal is also known as the "future value," or the "maturity value" of the loan.[3]
  4. Learn the difference between simple interest and compound interest. You've just calculated simple interest, in which you only pay interest on the principal you borrowed. Many credit cards and other loans, however, utilize compound interest, where the interest you owe gathers interest of its own. Compound interest can result in much higher interest over time than simple interest. Calculating compound interest requires a different formula. Here's a side-by-side comparison of the two systems:
    • You take a loan out for $100 at 30% simple interest. You'll owe $30 interest after the first time period, $60 after the second, $90 after the third, and $120 after the fourth.
    • You take out a second loan of $100 at 30% compound interest. You'll owe $30 interest after the first time period, then $69, then $119.70, then $285.61.
    • Multiple other factors can come into play when calculating more complex forms of interest, including credit risk and inflation.



Tips

  • Other resources may use different variable names in this equation, but they will refer to the same figures and concepts as we do here.
  • Although this article should equip you with the skills and knowledge to calculate simple interest, there are multiple online interest calculators available for your use if you still need assistance.
  • This formula can be rearranged to allow you to work out the Principal (<math>P=I/RT</math>), Rate (<math>R=I/PT</math>) or Time (<math>T=I/PR</math>)

Related Articles

Sources and Citations

  1. ↑ https://www.mathsisfun.com/money/interest.html
  2. ↑ http://www.investopedia.com/terms/o/opportunitycost.asp
  3. ↑ http://study.com/academy/lesson/how-to-find-simple-interest-rate-definition-formula-examples.html
Retrieved from "https://kipkis.com/index.php?title=Calculate_Simple_Interest&oldid=351263"