{"id":2404,"date":"2023-05-09T19:36:10","date_gmt":"2023-05-09T19:36:10","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=2404"},"modified":"2024-11-05T23:01:06","modified_gmt":"2024-11-05T23:01:06","slug":"simple-and-compound-interest-learn-it-1","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/simple-and-compound-interest-learn-it-1\/","title":{"raw":"Simple and Compound Interest: Learn It 1","rendered":"Simple and Compound Interest: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Calculate simple interest and compound interest<\/li>\r\n\t<li>Determine annual percentage yield (APY) based on given interest scenarios<\/li>\r\n\t<li>Solve for time in compound interest calculations<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Principal and Interest<\/h2>\r\n<p>Discussing interest starts with the <strong>principal<\/strong>, or amount your account starts with. This could be a starting investment, or the starting amount of a loan. Interest, in its most simple form, is calculated as a percent of the principal.\u00a0<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>principal and simple interest<\/h3>\r\n<p><strong>Principal <\/strong>is the amount of money that is borrowed or invested.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p><strong>Simple interest<\/strong> is the interest that is calculated only on the principal amount.<\/p>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox example\">\r\n<p>For example, if you borrowed [latex]$100[\/latex] from a friend and agree to repay it with [latex]5\\%[\/latex] interest, then the amount of interest you would pay would just be:<\/p>\r\n<center>[latex]5\\%[\/latex] of [latex]100[\/latex]: [latex]$100(0.05) = $5[\/latex]<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>The total amount you would repay would be [latex]$105[\/latex], the original principal plus the interest.<\/p>\r\n<\/section>\r\n<section class=\"textbox recall\">To convert a percent to a decimal, remove the [latex]\\%[\/latex] symbol and move the decimal place two places to the left. Ex. [latex]5\\% = 0.05[\/latex],\u00a0 [latex]25\\% = 0.25[\/latex], and [latex]100\\% = 1.0[\/latex]. To take [latex]5\\%[\/latex] of [latex]$100[\/latex] as in the paragraph above, write the percent as a decimal and translate the word <em>of<\/em> as multiplication.<br \/>\r\n<br \/>\r\nExample: [latex]5\\%[\/latex] of [latex]$100 \\Rightarrow 0.5\\cdot100=5[\/latex].<\/section>\r\n<h2>Simple One-Time Interest<\/h2>\r\n<p>Simple one-time interest refers to the interest that is earned or paid on a principal amount over a single period of time. This means that interest is only calculated once, at the end of the specified period, and it is based on the initial principal amount. Simple one-time interest is typically used in situations where the length of the investment or loan period is short and the interest rate is fixed.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>simple one-time interest<\/h3>\r\n<p>To calculate simple one-time interest use the following equations:<\/p>\r\n<p>&nbsp;<\/p>\r\n<center>[latex]\\begin{align}&amp;I={{P}_{0}}r\\\\&amp;A={{P}_{0}}+I={{P}_{0}}+{{P}_{0}}r={{P}_{0}}(1+r)\\\\\\end{align}[\/latex]<\/center>\r\n<p>&nbsp;<\/p>\r\n<ul>\r\n\t<li>[latex]I[\/latex] is the interest<\/li>\r\n\t<li>[latex]\\begin{align}{{P}_{0}}\\\\\\end{align}[\/latex] is the principal (starting amount)<\/li>\r\n\t<li>[latex]r[\/latex] is the interest rate (in decimal form. Example: [latex]5\\% = 0.05[\/latex])<\/li>\r\n\t<li>[latex]A[\/latex] is the end amount: principal plus interest<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox example\">A friend asks to borrow [latex]$300[\/latex] and agrees to repay it in [latex]30[\/latex] days with [latex]3\\%[\/latex] interest. How much interest will you earn?<br \/>\r\n[reveal-answer q=\"227650\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"227650\"]\r\n\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\begin{align}{{P}_{0}}\\\\\\end{align} = $300[\/latex]<\/td>\r\n<td>the principal<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]r = 0.03[\/latex]<\/td>\r\n<td>[latex]3\\%[\/latex] rate<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]I = $300(0.03) = $9.[\/latex]<\/td>\r\n<td>You will earn [latex]$9[\/latex] interest.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>&nbsp;<\/p>\r\n<p>The following video works through this example in detail.<\/p>\r\n<p>[embed]https:\/\/youtu.be\/TJYq7XGB8EY[\/embed]<\/p>\r\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/One+time+simple+interest.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cOne time simple interest\u201d here (opens in new window).<\/a><\/p>\r\n\r\n[\/hidden-answer]<\/section>\r\n<h2>Simple Interest Over Time<\/h2>\r\n<p>One-time simple interest is only common for extremely short-term loans. For longer-term loans, it is common for interest to be paid on a daily, monthly, quarterly, or annual basis. In that case, interest would be accrued (gathered) regularly.<\/p>\r\n<p>For example, bonds are essentially a loan made to the bond issuer (a company or government) by you, the bondholder. In return for the loan, the issuer agrees to pay interest, often annually. Bonds have a maturity date, at which time the issuer pays back the original bond value.<\/p>\r\n<p>We can generalize this idea of simple interest over time.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>simple interest over time<\/h3>\r\n<p style=\"text-align: center;\">[latex]\\begin{align}&amp;I={{P}_{0}}rt\\\\&amp;A={{P}_{0}}+I={{P}_{0}}+{{P}_{0}}rt={{P}_{0}}(1+rt)\\\\\\end{align}[\/latex]<\/p>\r\n<p>&nbsp;<\/p>\r\n<ul>\r\n\t<li>[latex]I[\/latex] is the interest<\/li>\r\n\t<li>[latex]\\begin{align}{{P}_{0}}\\\\\\end{align}[\/latex] is the principal (starting amount)<\/li>\r\n\t<li>[latex]r[\/latex] is the interest rate in decimal form<\/li>\r\n\t<li>[latex]t[\/latex] is time<\/li>\r\n\t<li>[latex]A[\/latex] is the end amount: principal plus interest<\/li>\r\n<\/ul>\r\n<p>The units of measurement (years, months, etc.) for the time should match the time period for the interest rate.<\/p>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox youChoose\">[videopicker divId=\"tnh-video-picker\" title=\"Simple Interest\" label=\"Select Video\"]<br \/>\r\n[videooption displayName=\"How to Calculate Simple Interest\" value=\"\/\/plugin.3playmedia.com\/show?mf=12451762&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=P4XOQgE6zq8&amp;video_target=tpm-plugin-eyzsffq3-P4XOQgE6zq8\"][videooption displayName=\"GCSE Maths - How to Calculate Simple Interest\" value=\"\/\/plugin.3playmedia.com\/show?mf=12451763&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=fqDOKz2m5rY&amp;video_target=tpm-plugin-u7225je7-fqDOKz2m5rY\"] [videooption displayName=\"Simple Interest Formula\" value=\"\/\/plugin.3playmedia.com\/show?mf=12451764&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=NCYNXkbTTUo&amp;video_target=tpm-plugin-ebfhpva5-NCYNXkbTTUo\"]<br \/>\r\n[\/videopicker]\r\n\r\n<p>&nbsp;<\/p>\r\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/How+to+Calculate+Simple+Interest.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cHow to Calculate Simple Interest\u201d here (opens in new window).<\/a><\/p>\r\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/GCSE+Maths+-+How+to+Calculate+Simple+Interest+%2395.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cGCSE Maths - How to Calculate Simple Interest #95\u201d here (opens in new window).<\/a><\/p>\r\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Simple+Interest+Formula.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cSimple Interest Formula\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<p>You have probably heard the terms APR and APY before, but do you know what they mean? APR (Annual Percentage Rate) and APY (Annual Percentage Yield) are both ways to measure the interest rate on a loan or investment. APR is typically used to describe the interest rate on a loan or credit card. While, APY is used to describe the interest rate on an investment, such as a savings account or CD.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>APR versus APY<\/h3>\r\n<p><span style=\"font-size: 12pt;\"><strong>APR \u2013 Annual Percentage Rate:<\/strong>\u00a0<\/span> APR is for interest paid by consumers on loans.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p><span style=\"font-size: 12pt;\"><strong>APY \u2013 Annual Percentage Yield:<\/strong><\/span> APY is for interest paid to consumers on savings.<\/p>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox proTip\">\r\n<p>Interest rates are usually given as an annual percentage yield (APY) \u2013 the total interest that will be paid in the year. If the interest is paid in smaller time increments, the APY will be divided up.<\/p>\r\n<p>For example, a [latex]6\\%[\/latex] APY paid monthly would be divided into twelve [latex]0.5\\%[\/latex] payments.<\/p>\r\n<p style=\"text-align: center;\">[latex]6\\div{12}=0.5[\/latex]<\/p>\r\n<p>A [latex]4\\%[\/latex] annual rate paid quarterly would be divided into four [latex]1\\%[\/latex] payments.<\/p>\r\n<p style=\"text-align: center;\">[latex]4\\div{4}=1[\/latex]<\/p>\r\n<\/section>\r\n<section class=\"textbox example\">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 [latex]4\\%[\/latex] annual rate, paid semi-annually, with a maturity in [latex]4[\/latex] years. How much interest will you earn?<br \/>\r\n[reveal-answer q=\"529216\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"529216\"]Since interest is being paid semi-annually (twice a year), the [latex]4\\%[\/latex] interest will be divided into two [latex]2\\%[\/latex] payments.\r\n\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\begin{align}{{P}_{0}}\\\\\\end{align}[\/latex][latex] = $1000[\/latex]<\/td>\r\n<td>the principal<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]r= 0.02[\/latex]<\/td>\r\n<td>[latex]2\\%[\/latex] rate per half-year<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]t = 8[\/latex]<\/td>\r\n<td>[latex]4[\/latex] years = [latex]8[\/latex] half-years<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]I = $1000(0.02)(8) = $160[\/latex].<\/td>\r\n<td>\u00a0You will earn [latex]$160[\/latex] interest total over the four years.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>&nbsp;<\/p>\r\n<p>This video explains the solution.<\/p>\r\n<p>[embed]https:\/\/youtu.be\/IfVn20go7-Y[\/embed]<\/p>\r\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Simple+interest+T-note+example.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cSimple interest T-note example\u201d here (opens in new window).<\/a><\/p>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox example\">A loan company charges [latex]$30[\/latex] interest for a one month loan of [latex]$500[\/latex]. Find the annual interest rate they are charging.<br \/>\r\n[reveal-answer q=\"288479\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"288479\"][latex]I = $30[\/latex] of interest<br \/>\r\n[latex]P_0 = $500[\/latex] principal<br \/>\r\n[latex]r =[\/latex] unknown<br \/>\r\n[latex]t = 1[\/latex] month<br \/>\r\n<br \/>\r\nUsing [latex]I = P_0rt[\/latex], we get [latex]30 = 500\u00b7r\u00b71[\/latex]. Solving, we get [latex]r = 0.06[\/latex], or [latex]6\\%[\/latex]. Since the time was monthly, this is the monthly interest. The annual rate would be [latex]12[\/latex] times this: [latex]72\\%[\/latex] interest.[\/hidden-answer]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]6934[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]6935[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Calculate simple interest and compound interest<\/li>\n<li>Determine annual percentage yield (APY) based on given interest scenarios<\/li>\n<li>Solve for time in compound interest calculations<\/li>\n<\/ul>\n<\/section>\n<h2>Principal and Interest<\/h2>\n<p>Discussing interest starts with the <strong>principal<\/strong>, or amount your account starts with. This could be a starting investment, or the starting amount of a loan. Interest, in its most simple form, is calculated as a percent of the principal.\u00a0<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>principal and simple interest<\/h3>\n<p><strong>Principal <\/strong>is the amount of money that is borrowed or invested.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Simple interest<\/strong> is the interest that is calculated only on the principal amount.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox example\">\n<p>For example, if you borrowed [latex]$100[\/latex] from a friend and agree to repay it with [latex]5\\%[\/latex] interest, then the amount of interest you would pay would just be:<\/p>\n<div style=\"text-align: center;\">[latex]5\\%[\/latex] of [latex]100[\/latex]: [latex]$100(0.05) = $5[\/latex]<\/div>\n<p>&nbsp;<\/p>\n<p>The total amount you would repay would be [latex]$105[\/latex], the original principal plus the interest.<\/p>\n<\/section>\n<section class=\"textbox recall\">To convert a percent to a decimal, remove the [latex]\\%[\/latex] symbol and move the decimal place two places to the left. Ex. [latex]5\\% = 0.05[\/latex],\u00a0 [latex]25\\% = 0.25[\/latex], and [latex]100\\% = 1.0[\/latex]. To take [latex]5\\%[\/latex] of [latex]$100[\/latex] as in the paragraph above, write the percent as a decimal and translate the word <em>of<\/em> as multiplication.<\/p>\n<p>Example: [latex]5\\%[\/latex] of [latex]$100 \\Rightarrow 0.5\\cdot100=5[\/latex].<\/section>\n<h2>Simple One-Time Interest<\/h2>\n<p>Simple one-time interest refers to the interest that is earned or paid on a principal amount over a single period of time. This means that interest is only calculated once, at the end of the specified period, and it is based on the initial principal amount. Simple one-time interest is typically used in situations where the length of the investment or loan period is short and the interest rate is fixed.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>simple one-time interest<\/h3>\n<p>To calculate simple one-time interest use the following equations:<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;\">[latex]\\begin{align}&I={{P}_{0}}r\\\\&A={{P}_{0}}+I={{P}_{0}}+{{P}_{0}}r={{P}_{0}}(1+r)\\\\\\end{align}[\/latex]<\/div>\n<p>&nbsp;<\/p>\n<ul>\n<li>[latex]I[\/latex] is the interest<\/li>\n<li>[latex]\\begin{align}{{P}_{0}}\\\\\\end{align}[\/latex] is the principal (starting amount)<\/li>\n<li>[latex]r[\/latex] is the interest rate (in decimal form. Example: [latex]5\\% = 0.05[\/latex])<\/li>\n<li>[latex]A[\/latex] is the end amount: principal plus interest<\/li>\n<\/ul>\n<\/div>\n<\/section>\n<section class=\"textbox example\">A friend asks to borrow [latex]$300[\/latex] and agrees to repay it in [latex]30[\/latex] days with [latex]3\\%[\/latex] interest. How much interest will you earn?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q227650\">Show Solution<\/button><\/p>\n<div id=\"q227650\" class=\"hidden-answer\" style=\"display: none\">\n<table>\n<tbody>\n<tr>\n<td>[latex]\\begin{align}{{P}_{0}}\\\\\\end{align} = $300[\/latex]<\/td>\n<td>the principal<\/td>\n<\/tr>\n<tr>\n<td>[latex]r = 0.03[\/latex]<\/td>\n<td>[latex]3\\%[\/latex] rate<\/td>\n<\/tr>\n<tr>\n<td>[latex]I = $300(0.03) = $9.[\/latex]<\/td>\n<td>You will earn [latex]$9[\/latex] interest.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>The following video works through this example in detail.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"One time simple interest\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/TJYq7XGB8EY?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/One+time+simple+interest.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cOne time simple interest\u201d here (opens in new window).<\/a><\/p>\n<\/div>\n<\/div>\n<\/section>\n<h2>Simple Interest Over Time<\/h2>\n<p>One-time simple interest is only common for extremely short-term loans. For longer-term loans, it is common for interest to be paid on a daily, monthly, quarterly, or annual basis. In that case, interest would be accrued (gathered) regularly.<\/p>\n<p>For example, bonds are essentially a loan made to the bond issuer (a company or government) by you, the bondholder. In return for the loan, the issuer agrees to pay interest, often annually. Bonds have a maturity date, at which time the issuer pays back the original bond value.<\/p>\n<p>We can generalize this idea of simple interest over time.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>simple interest over time<\/h3>\n<p style=\"text-align: center;\">[latex]\\begin{align}&I={{P}_{0}}rt\\\\&A={{P}_{0}}+I={{P}_{0}}+{{P}_{0}}rt={{P}_{0}}(1+rt)\\\\\\end{align}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li>[latex]I[\/latex] is the interest<\/li>\n<li>[latex]\\begin{align}{{P}_{0}}\\\\\\end{align}[\/latex] is the principal (starting amount)<\/li>\n<li>[latex]r[\/latex] is the interest rate in decimal form<\/li>\n<li>[latex]t[\/latex] is time<\/li>\n<li>[latex]A[\/latex] is the end amount: principal plus interest<\/li>\n<\/ul>\n<p>The units of measurement (years, months, etc.) for the time should match the time period for the interest rate.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox youChoose\">\n<div id=\"tnh-video-picker\" class=\"videoPicker\">\n<h3>Simple Interest<\/h3>\n<form><label>Select Video:<\/label><select name=\"video\"><option value=\"\/\/plugin.3playmedia.com\/show?mf=12451762&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=P4XOQgE6zq8&amp;video_target=tpm-plugin-eyzsffq3-P4XOQgE6zq8&#8243;\">How to Calculate Simple Interest<\/option><option value=\"\/\/plugin.3playmedia.com\/show?mf=12451763&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=fqDOKz2m5rY&amp;video_target=tpm-plugin-u7225je7-fqDOKz2m5rY\">GCSE Maths &#8211; How to Calculate Simple Interest<\/option><option value=\"\/\/plugin.3playmedia.com\/show?mf=12451764&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=NCYNXkbTTUo&amp;video_target=tpm-plugin-ebfhpva5-NCYNXkbTTUo\">Simple Interest Formula<\/option><\/select><\/form>\n<div class=\"videoContainer threePlay\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=12451762&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=P4XOQgE6zq8&amp;video_target=tpm-plugin-eyzsffq3-P4XOQgE6zq8&#8243;\" allowfullscreen><\/iframe><\/div>\n<p>&nbsp;<\/p>\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/How+to+Calculate+Simple+Interest.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cHow to Calculate Simple Interest\u201d here (opens in new window).<\/a><\/p>\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/GCSE+Maths+-+How+to+Calculate+Simple+Interest+%2395.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cGCSE Maths &#8211; How to Calculate Simple Interest #95\u201d here (opens in new window).<\/a><\/p>\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Simple+Interest+Formula.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cSimple Interest Formula\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<p>You have probably heard the terms APR and APY before, but do you know what they mean? APR (Annual Percentage Rate) and APY (Annual Percentage Yield) are both ways to measure the interest rate on a loan or investment. APR is typically used to describe the interest rate on a loan or credit card. While, APY is used to describe the interest rate on an investment, such as a savings account or CD.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>APR versus APY<\/h3>\n<p><span style=\"font-size: 12pt;\"><strong>APR \u2013 Annual Percentage Rate:<\/strong>\u00a0<\/span> APR is for interest paid by consumers on loans.<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 12pt;\"><strong>APY \u2013 Annual Percentage Yield:<\/strong><\/span> APY is for interest paid to consumers on savings.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox proTip\">\n<p>Interest rates are usually given as an annual percentage yield (APY) \u2013 the total interest that will be paid in the year. If the interest is paid in smaller time increments, the APY will be divided up.<\/p>\n<p>For example, a [latex]6\\%[\/latex] APY paid monthly would be divided into twelve [latex]0.5\\%[\/latex] payments.<\/p>\n<p style=\"text-align: center;\">[latex]6\\div{12}=0.5[\/latex]<\/p>\n<p>A [latex]4\\%[\/latex] annual rate paid quarterly would be divided into four [latex]1\\%[\/latex] payments.<\/p>\n<p style=\"text-align: center;\">[latex]4\\div{4}=1[\/latex]<\/p>\n<\/section>\n<section class=\"textbox example\">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 [latex]4\\%[\/latex] annual rate, paid semi-annually, with a maturity in [latex]4[\/latex] years. How much interest will you earn?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q529216\">Show Solution<\/button><\/p>\n<div id=\"q529216\" class=\"hidden-answer\" style=\"display: none\">Since interest is being paid semi-annually (twice a year), the [latex]4\\%[\/latex] interest will be divided into two [latex]2\\%[\/latex] payments.<\/p>\n<table>\n<tbody>\n<tr>\n<td>[latex]\\begin{align}{{P}_{0}}\\\\\\end{align}[\/latex][latex]= $1000[\/latex]<\/td>\n<td>the principal<\/td>\n<\/tr>\n<tr>\n<td>[latex]r= 0.02[\/latex]<\/td>\n<td>[latex]2\\%[\/latex] rate per half-year<\/td>\n<\/tr>\n<tr>\n<td>[latex]t = 8[\/latex]<\/td>\n<td>[latex]4[\/latex] years = [latex]8[\/latex] half-years<\/td>\n<\/tr>\n<tr>\n<td>[latex]I = $1000(0.02)(8) = $160[\/latex].<\/td>\n<td>\u00a0You will earn [latex]$160[\/latex] interest total over the four years.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>This video explains the solution.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Simple interest T-note example\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/IfVn20go7-Y?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Simple+interest+T-note+example.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cSimple interest T-note example\u201d here (opens in new window).<\/a><\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">A loan company charges [latex]$30[\/latex] interest for a one month loan of [latex]$500[\/latex]. Find the annual interest rate they are charging.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q288479\">Show Solution<\/button><\/p>\n<div id=\"q288479\" class=\"hidden-answer\" style=\"display: none\">[latex]I = $30[\/latex] of interest<br \/>\n[latex]P_0 = $500[\/latex] principal<br \/>\n[latex]r =[\/latex] unknown<br \/>\n[latex]t = 1[\/latex] month<\/p>\n<p>Using [latex]I = P_0rt[\/latex], we get [latex]30 = 500\u00b7r\u00b71[\/latex]. Solving, we get [latex]r = 0.06[\/latex], or [latex]6\\%[\/latex]. Since the time was monthly, this is the monthly interest. The annual rate would be [latex]12[\/latex] times this: [latex]72\\%[\/latex] interest.<\/p><\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm6934\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=6934&theme=lumen&iframe_resize_id=ohm6934&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm6935\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=6935&theme=lumen&iframe_resize_id=ohm6935&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":15,"menu_order":19,"template":"","meta":{"_candela_citation":"[{\"type\":\"copyrighted_video\",\"description\":\"How to Calculate Simple Interest\",\"author\":\"wikiHow\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/P4XOQgE6zq8\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"\"},{\"type\":\"copyrighted_video\",\"description\":\"GCSE Maths - 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