{"id":10448,"date":"2017-05-26T20:42:37","date_gmt":"2017-05-26T20:42:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10448"},"modified":"2024-04-30T16:43:19","modified_gmt":"2024-04-30T16:43:19","slug":"using-the-simple-interest-formula-to-calculate-rate-of-interest-or-principal","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/using-the-simple-interest-formula-to-calculate-rate-of-interest-or-principal\/","title":{"raw":"Applications With Simple Interest","rendered":"Applications With Simple Interest"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Solve simple interest applications<\/li>\r\n<\/ul>\r\n<\/div>\r\nApplications with simple interest usually involve either investing money or borrowing money. To solve these applications, we continue to use the same strategy for applications that we have used earlier in this chapter. The only difference is that in place of translating to get an equation, we can use the simple interest formula. We will provide examples of how to find interest earned, calculate the rate of interest, and how to find the principal given a rate and the interest earned.\r\n<h3>Calculating Interest Earned<\/h3>\r\nWe will start by solving a simple interest application to find the interest.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nNathalie deposited [latex]\\text{\\$12,500}[\/latex] in her bank account where it will earn [latex]\\text{4%}[\/latex] interest. How much interest will Nathalie earn in [latex]5[\/latex] years?\r\n\r\nSolution\r\nWe are asked to find the Interest, [latex]I[\/latex].\r\nOrganize the given information in a list.\r\n\r\nInterest: [latex]I=[\/latex] unknown\r\n\r\nPrincipal: [latex]P=$12,500[\/latex]\r\n\r\nRate: [latex]r=4\\%=0.04[\/latex]\r\n\r\nTime: [latex]t=5[\/latex] years\r\n<table id=\"eip-id1168467172609\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Write the formula.<\/td>\r\n<td>[latex]I=Prt[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute the given information.<\/td>\r\n<td>[latex]I=\\left(12,500\\right)\\left(0.04\\right)\\left(5\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]I=2,500[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check your answer. Is [latex]\\text{\\$2,500}[\/latex] a reasonable interest on [latex]\\text{\\$12,500}[\/latex] over [latex]5[\/latex] years?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>At [latex]4\\text{%}[\/latex] interest per year, in [latex]5[\/latex] years the interest would be [latex]20\\text{%}[\/latex] of the principal. Is [latex]20\\text{%}[\/latex] of [latex]\\text{\\$12,500}[\/latex] equal to [latex]\\text{\\$2,500}[\/latex]? Yes.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>The interest is [latex]\\text{\\$2,500}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146792[\/ohm_question]\r\n\r\n<\/div>\r\n<h3>Calculating Rate<\/h3>\r\nThere may be times when you know the amount of interest earned on a given principal over a certain length of time, but you don't know the rate. For instance, this might happen when family members lend or borrow money among themselves instead of dealing with a bank. In the next example, we'll show how to solve for the rate.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nLoren lent his brother [latex]\\text{\\$3,000}[\/latex] to help him buy a car. In [latex]\\text{4 years}[\/latex] his brother paid him back the [latex]\\text{\\$3,000}[\/latex] plus [latex]\\text{\\$660}[\/latex] in interest. What was the rate of interest?\r\n[reveal-answer q=\"361018\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"361018\"]\r\n\r\nSolution\r\nWe are asked to find the rate of interest, [latex]r[\/latex].\r\nOrganize the given information.\r\n\r\n[latex]\\begin{array}{ccc}\\hfill I&amp; =&amp; \\text{\\$660}\\hfill \\\\ \\hfill P&amp; =&amp; \\text{\\$3,000}\\hfill \\\\ \\hfill r&amp; =&amp; ?\\hfill \\\\ \\hfill t&amp; =&amp; \\text{4 years}\\hfill \\end{array}[\/latex]\r\n<table id=\"eip-id1168467260736\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Write the formula.<\/td>\r\n<td>[latex]I=Prt[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute the given information.<\/td>\r\n<td>[latex]660=\\left(3,000\\right)r\\left(4\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]660=\\left(12,000\\right)r[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td>[latex]\\dfrac{660}{12,000}\\normalsize=\\dfrac{\\left(12,000\\right)r}{12,000}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]0.055=r[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change to percent form.<\/td>\r\n<td>[latex]\\text{5.5%}=r[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check your answer. Is [latex]5.5\\text{%}[\/latex] a reasonable interest rate to pay your brother?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]I=Prt[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]660\\stackrel{?}{=}\\left(3,000\\right)\\left(0.055\\right)\\left(4\\right)[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]660=660\\quad\\checkmark [\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>The rate of interest was [latex]5.5\\text{%}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146793[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next video we use the simple interest formula to find the rate of interest given an amount of money borrowed and the amount if interest paid.\r\n\r\nhttps:\/\/youtu.be\/SgnE7BJQG10\r\n<h3>Calculating Principal<\/h3>\r\nThere may be times when you take a loan for a large purchase and the amount of the principal is not clear. This might happen, for instance, in making a car purchase when the dealer adds the cost of a warranty to the price of the car. In the next example, we will solve a simple interest application for the principal.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nEduardo noticed that his new car loan papers stated that with an interest rate of [latex]\\text{7.5%}[\/latex], he would pay [latex]\\text{\\$6,596.25}[\/latex] in interest over [latex]5[\/latex] years. How much did he borrow to pay for his car?\r\n[reveal-answer q=\"754756\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"754756\"]\r\n\r\nSolution\r\nWe are asked to find the principal, [latex]P[\/latex].\r\nOrganize the given information.\r\n[latex]\\begin{array}{ccc}\\hfill I&amp; =&amp; 6,596.25\\hfill \\\\ \\hfill P&amp; =&amp; ?\\hfill \\\\ \\hfill r&amp; =&amp; \\text{7.5%}\\hfill \\\\ \\hfill t&amp; =&amp; \\text{5 years}\\hfill \\end{array}[\/latex]\r\n<table id=\"eip-id1168466205229\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Write the formula.<\/td>\r\n<td>[latex]I=Prt[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute the given information.<\/td>\r\n<td>[latex]6,596.25=P\\left(0.075\\right)\\left(5\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]6,596.25=0.375P[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td>[latex]\\dfrac{6,596.25}{0.375}\\normalsize=\\dfrac{0.375P}{0.375}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]17,590=P[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check your answer. Is [latex]\\text{\\$17,590}[\/latex] a reasonable amount to borrow to buy a car?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]I=Prt[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]6,596.25\\stackrel{?}{=}\\left(17,590\\right)\\left(0.075\\right)\\left(5\\right)[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]6,596.25=6,596.25\\quad\\checkmark [\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>The amount borrowed was [latex]\\text{\\$17,590}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\n[ohm_question]146794[\/ohm_question]\r\n\r\n<\/div>\r\nIn the simple interest formula, the rate of interest is given as an annual rate, the rate for one year. So the units of time must be in years. If the time is given in months, we convert it to years.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nCaroline got [latex]\\text{\\$900}[\/latex] as graduation gifts and invested it in a [latex]\\text{10-month}[\/latex] certificate of deposit that earned [latex]\\text{2.1%}[\/latex] interest. How much interest did this investment earn?\r\n[reveal-answer q=\"799758\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"799758\"]\r\n\r\nSolution\r\nWe are asked to find the interest, [latex]I[\/latex].\r\nOrganize the given information.\r\n[latex]\\begin{array}{ccc}\\hfill I&amp; =&amp; ?\\hfill \\\\ \\hfill P&amp; =&amp; \\text{\\$900}\\hfill \\\\ \\hfill r&amp; =&amp; \\text{2.1%}\\hfill \\\\ \\hfill t&amp; =&amp; \\text{10 months}\\hfill \\end{array}[\/latex]\r\n<table id=\"eip-id1168467203804\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Write the formula.<\/td>\r\n<td>[latex]I=Prt[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute the given information, converting 10 months to [latex]\\dfrac{10}{12}[\/latex] of a year.<\/td>\r\n<td>[latex]I=$900\\left(0.021\\right)\\left(\\dfrac{10}{12}\\normalsize\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]I=15.75[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check your answer. Is [latex]\\text{\\$15.75}[\/latex] a reasonable amount of interest?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>If Caroline had invested the [latex]\\text{\\$900}[\/latex] for a full year at [latex]2\\text{%}[\/latex] interest, the amount of interest would have been [latex]\\text{\\$18}[\/latex]. Yes, [latex]\\text{\\$15.75}[\/latex] is reasonable.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>The interest earned was [latex]\\text{\\$15.75}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146796[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nA friend asks to borrow [latex]$240[\/latex], offering to repay you [latex]$250[\/latex] in 1 month. What annual interest rate is this equivalent to?\r\n\r\n[reveal-answer q=\"470866\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"470866\"]Identify the information given in the problem. Here your friend is paying back $10 more than he borrowed, so that is the interest paid.\r\n\r\n[latex]\\begin{array}{ccc}\\hfill I&amp; =&amp; \\text{\\$10}\\hfill \\\\ \\hfill P&amp; =&amp; \\text{\\$240}\\hfill \\\\ \\hfill r&amp; =&amp; ?\\hfill \\\\ \\hfill t&amp; =&amp; \\text{1 month}\\hfill \\end{array}[\/latex]\r\n\r\nConvert the time to years.\r\n<p style=\"text-align: center;\">[latex]1\\,\\,\\text{month}=\\frac{1}{12}\\,\\,\\text{year}[\/latex]<\/p>\r\nPut the information in the simple interest equation.\r\n<p style=\"text-align: center;\">[latex]10=240\\cdot{r}\\cdot\\frac{1}{12}[\/latex]<\/p>\r\nRegroup and simplify.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}10=r\\cdot240\\cdot\\frac{1}{12}\\\\\\\\10=r\\cdot\\frac{240}{12}\\\\\\\\10=r\\cdot20\\end{array}[\/latex]<\/p>\r\n&nbsp;\r\n\r\nDivide to undo the multiplication.\r\n<p style=\"text-align: center;\">[latex]r=10\\div20=0.50[\/latex]<\/p>\r\nRewrite as a percent.\r\n<p style=\"text-align: center;\">[latex]0.50=50\\%[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\nThis is equivalent to a \u00a0[latex]50\\%[\/latex] annual interest rate.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe example video that follows shows how to determine the annual simple interest rate.\r\n\r\nhttps:\/\/youtu.be\/SgnE7BJQG10\r\n\r\nAnother application of interest rate is calculating Treasury Notes.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nTreasury Notes (T-notes) are bonds issued by the federal government to cover its expenses. Suppose you obtain a [latex]$1,000[\/latex] T-note with a \u00a0[latex]4\\%[\/latex] annual rate, with a maturity in \u00a0[latex]2[\/latex] years. How much interest will you earn?\r\n\r\n[reveal-answer q=\"694437\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"694437\"]Identify the information given in the problem.\r\n\r\n[latex]\\begin{array}{ccc}\\hfill I&amp; =&amp; \\text{?}\\hfill \\\\ \\hfill P&amp; =&amp; \\text{\\$1,000}\\hfill \\\\ \\hfill r&amp; =&amp; \\text{4% or 0.04}\\hfill \\\\ \\hfill t&amp; =&amp; \\text{2 years}\\hfill \\end{array}[\/latex]\r\n\r\nPut the information in the simple interest equation.\r\n<p style=\"text-align: center;\">[latex]I=1000\\cdot0.04\\cdot2[\/latex]<\/p>\r\nMultiply.\r\n<p style=\"text-align: center;\">[latex]I=80[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\nYou would earn [latex]$80[\/latex] in interest.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nin the following video we show an example of how to calculate the amount of interest earned on a treasury note.\r\n\r\nhttps:\/\/youtu.be\/iVmetUlbheY","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Solve simple interest applications<\/li>\n<\/ul>\n<\/div>\n<p>Applications with simple interest usually involve either investing money or borrowing money. To solve these applications, we continue to use the same strategy for applications that we have used earlier in this chapter. The only difference is that in place of translating to get an equation, we can use the simple interest formula. We will provide examples of how to find interest earned, calculate the rate of interest, and how to find the principal given a rate and the interest earned.<\/p>\n<h3>Calculating Interest Earned<\/h3>\n<p>We will start by solving a simple interest application to find the interest.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Nathalie deposited [latex]\\text{\\$12,500}[\/latex] in her bank account where it will earn [latex]\\text{4%}[\/latex] interest. How much interest will Nathalie earn in [latex]5[\/latex] years?<\/p>\n<p>Solution<br \/>\nWe are asked to find the Interest, [latex]I[\/latex].<br \/>\nOrganize the given information in a list.<\/p>\n<p>Interest: [latex]I=[\/latex] unknown<\/p>\n<p>Principal: [latex]P=$12,500[\/latex]<\/p>\n<p>Rate: [latex]r=4\\%=0.04[\/latex]<\/p>\n<p>Time: [latex]t=5[\/latex] years<\/p>\n<table id=\"eip-id1168467172609\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Write the formula.<\/td>\n<td>[latex]I=Prt[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute the given information.<\/td>\n<td>[latex]I=\\left(12,500\\right)\\left(0.04\\right)\\left(5\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]I=2,500[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Is [latex]\\text{\\$2,500}[\/latex] a reasonable interest on [latex]\\text{\\$12,500}[\/latex] over [latex]5[\/latex] years?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>At [latex]4\\text{%}[\/latex] interest per year, in [latex]5[\/latex] years the interest would be [latex]20\\text{%}[\/latex] of the principal. Is [latex]20\\text{%}[\/latex] of [latex]\\text{\\$12,500}[\/latex] equal to [latex]\\text{\\$2,500}[\/latex]? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The interest is [latex]\\text{\\$2,500}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146792\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146792&theme=oea&iframe_resize_id=ohm146792&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h3>Calculating Rate<\/h3>\n<p>There may be times when you know the amount of interest earned on a given principal over a certain length of time, but you don&#8217;t know the rate. For instance, this might happen when family members lend or borrow money among themselves instead of dealing with a bank. In the next example, we&#8217;ll show how to solve for the rate.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Loren lent his brother [latex]\\text{\\$3,000}[\/latex] to help him buy a car. In [latex]\\text{4 years}[\/latex] his brother paid him back the [latex]\\text{\\$3,000}[\/latex] plus [latex]\\text{\\$660}[\/latex] in interest. What was the rate of interest?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q361018\">Show Solution<\/span><\/p>\n<div id=\"q361018\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe are asked to find the rate of interest, [latex]r[\/latex].<br \/>\nOrganize the given information.<\/p>\n<p>[latex]\\begin{array}{ccc}\\hfill I& =& \\text{\\$660}\\hfill \\\\ \\hfill P& =& \\text{\\$3,000}\\hfill \\\\ \\hfill r& =& ?\\hfill \\\\ \\hfill t& =& \\text{4 years}\\hfill \\end{array}[\/latex]<\/p>\n<table id=\"eip-id1168467260736\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Write the formula.<\/td>\n<td>[latex]I=Prt[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute the given information.<\/td>\n<td>[latex]660=\\left(3,000\\right)r\\left(4\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]660=\\left(12,000\\right)r[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>[latex]\\dfrac{660}{12,000}\\normalsize=\\dfrac{\\left(12,000\\right)r}{12,000}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]0.055=r[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change to percent form.<\/td>\n<td>[latex]\\text{5.5%}=r[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Is [latex]5.5\\text{%}[\/latex] a reasonable interest rate to pay your brother?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]I=Prt[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]660\\stackrel{?}{=}\\left(3,000\\right)\\left(0.055\\right)\\left(4\\right)[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]660=660\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The rate of interest was [latex]5.5\\text{%}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146793\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146793&theme=oea&iframe_resize_id=ohm146793&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next video we use the simple interest formula to find the rate of interest given an amount of money borrowed and the amount if interest paid.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Determine a Simple Interest Rate For a Loan with Known Interest\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/SgnE7BJQG10?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Calculating Principal<\/h3>\n<p>There may be times when you take a loan for a large purchase and the amount of the principal is not clear. This might happen, for instance, in making a car purchase when the dealer adds the cost of a warranty to the price of the car. In the next example, we will solve a simple interest application for the principal.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Eduardo noticed that his new car loan papers stated that with an interest rate of [latex]\\text{7.5%}[\/latex], he would pay [latex]\\text{\\$6,596.25}[\/latex] in interest over [latex]5[\/latex] years. How much did he borrow to pay for his car?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q754756\">Show Solution<\/span><\/p>\n<div id=\"q754756\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe are asked to find the principal, [latex]P[\/latex].<br \/>\nOrganize the given information.<br \/>\n[latex]\\begin{array}{ccc}\\hfill I& =& 6,596.25\\hfill \\\\ \\hfill P& =& ?\\hfill \\\\ \\hfill r& =& \\text{7.5%}\\hfill \\\\ \\hfill t& =& \\text{5 years}\\hfill \\end{array}[\/latex]<\/p>\n<table id=\"eip-id1168466205229\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Write the formula.<\/td>\n<td>[latex]I=Prt[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute the given information.<\/td>\n<td>[latex]6,596.25=P\\left(0.075\\right)\\left(5\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]6,596.25=0.375P[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>[latex]\\dfrac{6,596.25}{0.375}\\normalsize=\\dfrac{0.375P}{0.375}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]17,590=P[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Is [latex]\\text{\\$17,590}[\/latex] a reasonable amount to borrow to buy a car?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]I=Prt[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]6,596.25\\stackrel{?}{=}\\left(17,590\\right)\\left(0.075\\right)\\left(5\\right)[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]6,596.25=6,596.25\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The amount borrowed was [latex]\\text{\\$17,590}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146794\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146794&theme=oea&iframe_resize_id=ohm146794&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the simple interest formula, the rate of interest is given as an annual rate, the rate for one year. So the units of time must be in years. If the time is given in months, we convert it to years.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Caroline got [latex]\\text{\\$900}[\/latex] as graduation gifts and invested it in a [latex]\\text{10-month}[\/latex] certificate of deposit that earned [latex]\\text{2.1%}[\/latex] interest. How much interest did this investment earn?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q799758\">Show Solution<\/span><\/p>\n<div id=\"q799758\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe are asked to find the interest, [latex]I[\/latex].<br \/>\nOrganize the given information.<br \/>\n[latex]\\begin{array}{ccc}\\hfill I& =& ?\\hfill \\\\ \\hfill P& =& \\text{\\$900}\\hfill \\\\ \\hfill r& =& \\text{2.1%}\\hfill \\\\ \\hfill t& =& \\text{10 months}\\hfill \\end{array}[\/latex]<\/p>\n<table id=\"eip-id1168467203804\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Write the formula.<\/td>\n<td>[latex]I=Prt[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute the given information, converting 10 months to [latex]\\dfrac{10}{12}[\/latex] of a year.<\/td>\n<td>[latex]I=$900\\left(0.021\\right)\\left(\\dfrac{10}{12}\\normalsize\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]I=15.75[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Is [latex]\\text{\\$15.75}[\/latex] a reasonable amount of interest?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>If Caroline had invested the [latex]\\text{\\$900}[\/latex] for a full year at [latex]2\\text{%}[\/latex] interest, the amount of interest would have been [latex]\\text{\\$18}[\/latex]. Yes, [latex]\\text{\\$15.75}[\/latex] is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The interest earned was [latex]\\text{\\$15.75}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146796\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146796&theme=oea&iframe_resize_id=ohm146796&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>A friend asks to borrow [latex]$240[\/latex], offering to repay you [latex]$250[\/latex] in 1 month. What annual interest rate is this equivalent to?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q470866\">Show Solution<\/span><\/p>\n<div id=\"q470866\" class=\"hidden-answer\" style=\"display: none\">Identify the information given in the problem. Here your friend is paying back $10 more than he borrowed, so that is the interest paid.<\/p>\n<p>[latex]\\begin{array}{ccc}\\hfill I& =& \\text{\\$10}\\hfill \\\\ \\hfill P& =& \\text{\\$240}\\hfill \\\\ \\hfill r& =& ?\\hfill \\\\ \\hfill t& =& \\text{1 month}\\hfill \\end{array}[\/latex]<\/p>\n<p>Convert the time to years.<\/p>\n<p style=\"text-align: center;\">[latex]1\\,\\,\\text{month}=\\frac{1}{12}\\,\\,\\text{year}[\/latex]<\/p>\n<p>Put the information in the simple interest equation.<\/p>\n<p style=\"text-align: center;\">[latex]10=240\\cdot{r}\\cdot\\frac{1}{12}[\/latex]<\/p>\n<p>Regroup and simplify.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}10=r\\cdot240\\cdot\\frac{1}{12}\\\\\\\\10=r\\cdot\\frac{240}{12}\\\\\\\\10=r\\cdot20\\end{array}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>Divide to undo the multiplication.<\/p>\n<p style=\"text-align: center;\">[latex]r=10\\div20=0.50[\/latex]<\/p>\n<p>Rewrite as a percent.<\/p>\n<p style=\"text-align: center;\">[latex]0.50=50\\%[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>This is equivalent to a \u00a0[latex]50\\%[\/latex] annual interest rate.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The example video that follows shows how to determine the annual simple interest rate.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Determine a Simple Interest Rate For a Loan with Known Interest\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/SgnE7BJQG10?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Another application of interest rate is calculating Treasury Notes.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Treasury Notes (T-notes) are bonds issued by the federal government to cover its expenses. Suppose you obtain a [latex]$1,000[\/latex] T-note with a \u00a0[latex]4\\%[\/latex] annual rate, with a maturity in \u00a0[latex]2[\/latex] years. How much interest will you earn?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q694437\">Show Solution<\/span><\/p>\n<div id=\"q694437\" class=\"hidden-answer\" style=\"display: none\">Identify the information given in the problem.<\/p>\n<p>[latex]\\begin{array}{ccc}\\hfill I& =& \\text{?}\\hfill \\\\ \\hfill P& =& \\text{\\$1,000}\\hfill \\\\ \\hfill r& =& \\text{4% or 0.04}\\hfill \\\\ \\hfill t& =& \\text{2 years}\\hfill \\end{array}[\/latex]<\/p>\n<p>Put the information in the simple interest equation.<\/p>\n<p style=\"text-align: center;\">[latex]I=1000\\cdot0.04\\cdot2[\/latex]<\/p>\n<p>Multiply.<\/p>\n<p style=\"text-align: center;\">[latex]I=80[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>You would earn [latex]$80[\/latex] in interest.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>in the following video we show an example of how to calculate the amount of interest earned on a treasury note.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Determine the Amount of Interest Earned (Simple Interest)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/iVmetUlbheY?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-10448\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID: 146792, 146793, 146794, 146796. <strong>Authored by<\/strong>: Alyson Day. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Determine the Amount of Interest Earned (Simple Interest). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/iVmetUlbheY\">https:\/\/youtu.be\/iVmetUlbheY<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Determine a Simple Interest Rate For a Loan with Known Interest. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/SgnE7BJQG10\">https:\/\/youtu.be\/SgnE7BJQG10<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":20,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Determine the Amount of Interest Earned (Simple Interest)\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/iVmetUlbheY\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Determine a Simple Interest Rate For a Loan with Known Interest\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/SgnE7BJQG10\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID: 146792, 146793, 146794, 146796\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"0c5044d98f5d4830971bfc94baeb5fed, 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