{"id":4106,"date":"2023-06-06T17:35:41","date_gmt":"2023-06-06T17:35:41","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=4106"},"modified":"2024-10-18T20:55:51","modified_gmt":"2024-10-18T20:55:51","slug":"homeownership-fresh-take","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/homeownership-fresh-take\/","title":{"raw":"Homeownership: Fresh Take","rendered":"Homeownership: Fresh Take"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Evaluate the pros and cons of renting and homeownership<\/li>\r\n\t<li>Calculate the monthly payment and interest expenses of a mortgage<\/li>\r\n\t<li>Interpret and understand an amortization schedule<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Homeownership Versus Renting<\/h2>\r\n<section class=\"textbox watchIt\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=10356038&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=tijZtwbiF7Y&amp;video_target=tpm-plugin-z4in505h-tijZtwbiF7Y\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Do+you+know+what+are+the+Pros+and+Cons+of+Renting+vs+Buying.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cDo you know what are the Pros and Cons of Renting vs Buying\u201d here (opens in new window).<\/a><\/p><\/section>\r\n<h2>Understanding and Calculating Mortgage Payments<\/h2>\r\n<div class=\"textbox shaded\">\r\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\r\n<p>A <strong>mortgage<\/strong> is a type of loan, typically used to purchase a home, where the property serves as the collateral. The mortgage payment comprises principal repayment and interest payment. The interest is the cost of borrowing the principal amount for the purchase.<\/p>\r\n<p>To calculate the monthly payment of a mortgage, you need to know the principal amount (the loan amount), the interest rate, and the loan term. The formula to calculate the monthly payment (PMT) on a mortgage is as follows:<\/p>\r\n<center>[latex] pmt=\\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121}[\/latex]<\/center>\r\n<p>&nbsp;<\/p>\r\n\r\nwhere [latex]PMT[\/latex] is the monthly mortgage payment, [latex]P[\/latex] is the principal loan amount, [latex]r[\/latex] is the annual interest rate in decimal form and [latex]t[\/latex] is the number of years of the payment.\r\n\r\n<p>To find the total amount of your payments over the life of the loan, multiply your monthly payments by the number of payments. The total paid, [latex]T[\/latex], on an [latex]t[\/latex] year mortgage with monthly payments [latex]pmt[\/latex] is [latex]T=pmt\\times12\\times t[\/latex].<\/p>\r\n<p>The cost of financing a mortgage, [latex]CoF[\/latex], is [latex]CoF=T\u2212P[\/latex] where [latex]P[\/latex] is the mortgage\u2019s starting principal and [latex]T[\/latex] is the total paid over the life of the mortgage.<\/p>\r\n<\/div>\r\n<section class=\"textbox example\">Paulo buys a house. His [latex]20[\/latex]-year mortgage comes to [latex]$153,899[\/latex] with [latex]4.21\\%[\/latex] interest. interest. Find Paulo's monthly payments.<br \/>\r\n[reveal-answer q=\"160930\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160930\"]<br \/>\r\nUsing the information above, [latex]P = $153,899[\/latex], [latex]r = 0.0421[\/latex] and [latex]t = 20[\/latex]. Substituting those values into the formula [latex] pmt=\\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121}[\/latex] and calculating, we find the payment is:\r\n\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{ll}<br \/>\r\nPMT &amp;&amp; = \\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121} \\\\<br \/>\r\n&amp;&amp; =\\frac{$153,899\\times\\frac{0.0421}{12}\\times(1+\\frac{0.0421}{12})^{12\\times 20}}{(1+\\frac{0.0421}{12})^{12\\times 20}\u22121} \\\\<br \/>\r\n&amp;&amp; =\\frac{$153,899\\times(.0035)\\times(1.0035)^{240}}{(1.0035)^{240}\u22121} \\\\<br \/>\r\n&amp;&amp; =\\frac{$1,245.874451}{1.312972331} \\\\<br \/>\r\n&amp;&amp; = \\$948.90 \\\\<br \/>\r\n\\end{array}[\/latex]<\/p>\r\n<br \/>\r\nHis mortgage payment is [latex]$948.90[\/latex].<br \/>\r\n<em>Note: Answers may vary slightly depending on how numbers were rounded.<\/em><br \/>\r\n[\/hidden-answer]<\/section>\r\n<section class=\"textbox example\">Arthur buys a house. Their [latex]15[\/latex]-year mortgage comes to [latex]$225,879[\/latex] with [latex]4.91\\%[\/latex] interest. If Arthur pays off the mortgage over those [latex]15[\/latex] years, how much will they have paid in total?<br \/>\r\n[reveal-answer q=\"160931\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160931\"]To find the total paid over the life of the mortgage, use the formula [latex]T=pmt\\times12\\times t[\/latex]. To calculate this, the payment must be found. Using the information above, [latex]P = $225,879[\/latex], [latex]r = 0.0491[\/latex] and [latex]t = 15[\/latex]. Substituting those values into the formula [latex] pmt=\\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121}[\/latex] and calculating, we find the payment is:\r\n\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{ll}<br \/>\r\nPMT &amp;&amp; = \\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121} \\\\<br \/>\r\n&amp;&amp; =\\frac{$$225,879\\times\\frac{0.0491}{12}\\times(1+\\frac{0.0491}{12})^{12\\times 15}}{(1+\\frac{0.0491}{12})^{12\\times 15}\u22121} \\\\<br \/>\r\n&amp;&amp; =\\frac{$225,879\\times(.004091\\overline{6})\\times(1.004091\\overline{6})^{180}}{(1.004091\\overline{6})^{180}\u22121} \\\\<br \/>\r\n&amp;&amp; =\\frac{$1927.439709}{1.085473955 } \\\\<br \/>\r\n&amp;&amp; = \\$1,775.67 \\\\<br \/>\r\n\\end{array}[\/latex]<\/p>\r\n<br \/>\r\nUsing the mortgage payment of [latex]$1,775.67 [\/latex] and [latex]t = 15[\/latex] years in the formula [latex]T=pmt\\times12\\times t[\/latex], the total that Arthur will pay for the mortgage is [latex]$319,618.80[\/latex].<br \/>\r\n<em>Note: Answers may vary slightly depending on how numbers were rounded.<\/em><br \/>\r\n[\/hidden-answer]<\/section>\r\n<section class=\"textbox example\">Arthur buys a house. Their [latex]15[\/latex]-year mortgage comes to [latex]$225,879[\/latex] with [latex]4.91\\%[\/latex] interest. What was Arthur's cost of financing?<br \/>\r\n[reveal-answer q=\"160932\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160932\"]We just found that the total that Arthur will pay for the [latex]$225,879[\/latex] mortgage is [latex]$319,618.80[\/latex]. (See previous example for the worked solution). <br \/>\r\n<br \/>\r\nSubtracting those we find the cost of financing [latex]CoF=T\u2212P = $319,618.80\u2212$225,879=$93,739.80[\/latex].<br \/>\r\n<em>Note: Answers may vary slightly depending on how numbers were rounded.<\/em><br \/>\r\n[\/hidden-answer]<\/section>\r\n<h3>Escrow Payments<\/h3>\r\n<div class=\"textbox shaded\">\r\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\r\n<p>An <strong>escrow account<\/strong> is a type of account that your mortgage lender sets up on your behalf when you close on your home. This account is used to pay certain property-related expenses on your behalf. The most common expenses that are paid out of an escrow account are property taxes and homeowners insurance. When you take out a mortgage, the lender typically divides the estimated annual cost of these expenses by [latex]12[\/latex] to determine a monthly amount. You then pay this amount as part of your monthly mortgage payment. The lender deposits these funds into the escrow account and then pays the expenses out of the account as they come due. This spreads out the cost of these large expenses into manageable monthly payments and ensures that these important bills are paid on time.<\/p>\r\n<\/div>\r\n<section class=\"textbox example\">Destiny decides to purchase a home, with a mortgage of [latex]$159,195.50[\/latex] at [latex]5.75\\%[\/latex] interest for [latex]30[\/latex] years. The assessed value of her home is [latex]$100,000[\/latex]. Her property taxes come to [latex]5.42\\%[\/latex] of her assessed value. Destiny also has to pay her home insurance every [latex]6[\/latex] months, and that comes to [latex]$843[\/latex] per [latex]6[\/latex] months. How much, including escrow, will Destiny pay per month?<br \/>\r\n[reveal-answer q=\"160936\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160936\"]<br \/>\r\nUsing the payment function to find Destiny's mortgage payments, [latex] pmt=\\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121}[\/latex], with [latex]P = $159,195.50[\/latex], [latex]r = 0.0575[\/latex] and [latex]t = 30[\/latex], her payments are:\r\n\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{ll}<br \/>\r\nPMT &amp;&amp; = \\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121} \\\\<br \/>\r\n&amp;&amp; =\\frac{$159,195.50\\times\\frac{0.0575}{12}\\times(1+\\frac{0.0575}{12})^{12\\times 30}}{(1+\\frac{0.0575}{12})^{12\\times 30}\u22121} \\\\<br \/>\r\n&amp;&amp; = \\$929.02 \\\\<br \/>\r\n\\end{array}[\/latex]<\/p>\r\n\r\nDestiny also pays into escrow [latex]\\frac{1}{12}[\/latex] of her property taxes per month. Her property taxes are [latex]5.42\\%[\/latex] of the assessed value of [latex]$100,000[\/latex], which comes to [latex]0.0542\\times$100,000=$5,420[\/latex]. This is an annual tax, so she pays [latex]\\frac{1}{12}[\/latex] of that each month, or [latex]$451.67[\/latex]. Destiny's home insurance is [latex]$843[\/latex] per [latex]6[\/latex] months, so each month she pays [latex]$140.50[\/latex] for insurance. <br \/>\r\n<br \/>\r\nAdding these together, her monthly payment is [latex]$929.02+$451.67+$140.50=$1,521.19[\/latex]. This is quite a bit more than the [latex]$929.02[\/latex] for the principal and interest.[\/hidden-answer]<\/section>\r\n<h2>Reading and Interpreting Amortization Tables<\/h2>\r\n<section class=\"textbox watchIt\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=10356039&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=E6amrtgENwY&amp;video_target=tpm-plugin-74xo56sx-E6amrtgENwY\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Amortization+Schedule+Explained.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cAmortization Schedule Explained\u201d here (opens in new window).<\/a><\/p><\/section>\r\n<section class=\"textbox example\">Below is a portion of an amortization table for a [latex]30[\/latex]-year, [latex]$228,320[\/latex] mortgage. Use that table to answer the following questions.<br \/>\r\n<center><img class=\"aligncenter size-full wp-image-4387\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/08161650\/CS_Photo_06_12_003.png\" alt=\"A spreadsheet labeled as amortization schedule calculator. The sheet calculates the repayment for the loan amount of $228,320.00 for an interest rate of 6.10 percent annually and the monthly payment is $1383.61 over 30 years. The factors include calculations such as month, payment, principal, interest, total, and interest and balance.\" width=\"603\" height=\"720\" \/><\/center>\r\n<p>&nbsp;<\/p>\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>What is the interest rate?<\/li>\r\n\t<li>How much are the payments?<\/li>\r\n\t<li>How much of payment [latex]235[\/latex] goes to principal?<\/li>\r\n\t<li>How much of payment [latex]215[\/latex] goes to interest?<\/li>\r\n\t<li>What\u2019s the remaining balance on the mortgage after payment [latex]227[\/latex]?<\/li>\r\n\t<li>At what payment does the amount that is applied to mortgage finally exceed the amount applied to interest?<\/li>\r\n<\/ol>\r\n<p>[reveal-answer q=\"160934\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"160934\"]<\/p>\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>Reading at the top of the table, we see the interest rate is [latex]6.1\\%[\/latex].<\/li>\r\n\t<li>Reading from the top of the table or from the column labeled Payment, we see the payments are [latex]$1,383.61[\/latex] per month.<\/li>\r\n\t<li>In the row for payment [latex]235[\/latex], we see that the amount that goes to principal is [latex]$730.38[\/latex].<\/li>\r\n\t<li>In the row for payment [latex]215[\/latex], we see that the amount that goes to interest is [latex]$723.66[\/latex].<\/li>\r\n\t<li>In the row for payment [latex]227[\/latex], we see the remaining balance is [latex]$133,513.05[\/latex].<\/li>\r\n\t<li>Payment [latex]225[\/latex].<\/li>\r\n<\/ol>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Evaluate the pros and cons of renting and homeownership<\/li>\n<li>Calculate the monthly payment and interest expenses of a mortgage<\/li>\n<li>Interpret and understand an amortization schedule<\/li>\n<\/ul>\n<\/section>\n<h2>Homeownership Versus Renting<\/h2>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=10356038&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=tijZtwbiF7Y&amp;video_target=tpm-plugin-z4in505h-tijZtwbiF7Y\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Do+you+know+what+are+the+Pros+and+Cons+of+Renting+vs+Buying.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cDo you know what are the Pros and Cons of Renting vs Buying\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h2>Understanding and Calculating Mortgage Payments<\/h2>\n<div class=\"textbox shaded\">\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\n<p>A <strong>mortgage<\/strong> is a type of loan, typically used to purchase a home, where the property serves as the collateral. The mortgage payment comprises principal repayment and interest payment. The interest is the cost of borrowing the principal amount for the purchase.<\/p>\n<p>To calculate the monthly payment of a mortgage, you need to know the principal amount (the loan amount), the interest rate, and the loan term. The formula to calculate the monthly payment (PMT) on a mortgage is as follows:<\/p>\n<div style=\"text-align: center;\">[latex]pmt=\\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121}[\/latex]<\/div>\n<p>&nbsp;<\/p>\n<p>where [latex]PMT[\/latex] is the monthly mortgage payment, [latex]P[\/latex] is the principal loan amount, [latex]r[\/latex] is the annual interest rate in decimal form and [latex]t[\/latex] is the number of years of the payment.<\/p>\n<p>To find the total amount of your payments over the life of the loan, multiply your monthly payments by the number of payments. The total paid, [latex]T[\/latex], on an [latex]t[\/latex] year mortgage with monthly payments [latex]pmt[\/latex] is [latex]T=pmt\\times12\\times t[\/latex].<\/p>\n<p>The cost of financing a mortgage, [latex]CoF[\/latex], is [latex]CoF=T\u2212P[\/latex] where [latex]P[\/latex] is the mortgage\u2019s starting principal and [latex]T[\/latex] is the total paid over the life of the mortgage.<\/p>\n<\/div>\n<section class=\"textbox example\">Paulo buys a house. His [latex]20[\/latex]-year mortgage comes to [latex]$153,899[\/latex] with [latex]4.21\\%[\/latex] interest. interest. Find Paulo&#8217;s monthly payments.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160930\">Show Solution<\/button><\/p>\n<div id=\"q160930\" class=\"hidden-answer\" style=\"display: none\">\nUsing the information above, [latex]P = $153,899[\/latex], [latex]r = 0.0421[\/latex] and [latex]t = 20[\/latex]. Substituting those values into the formula [latex]pmt=\\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121}[\/latex] and calculating, we find the payment is:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{ll}<br \/>  PMT && = \\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121} \\\\<br \/>  && =\\frac{$153,899\\times\\frac{0.0421}{12}\\times(1+\\frac{0.0421}{12})^{12\\times 20}}{(1+\\frac{0.0421}{12})^{12\\times 20}\u22121} \\\\<br \/>  && =\\frac{$153,899\\times(.0035)\\times(1.0035)^{240}}{(1.0035)^{240}\u22121} \\\\<br \/>  && =\\frac{$1,245.874451}{1.312972331} \\\\<br \/>  && = \\$948.90 \\\\<br \/>  \\end{array}[\/latex]<\/p>\n<p>\nHis mortgage payment is [latex]$948.90[\/latex].<br \/>\n<em>Note: Answers may vary slightly depending on how numbers were rounded.<\/em>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">Arthur buys a house. Their [latex]15[\/latex]-year mortgage comes to [latex]$225,879[\/latex] with [latex]4.91\\%[\/latex] interest. If Arthur pays off the mortgage over those [latex]15[\/latex] years, how much will they have paid in total?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160931\">Show Solution<\/button><\/p>\n<div id=\"q160931\" class=\"hidden-answer\" style=\"display: none\">To find the total paid over the life of the mortgage, use the formula [latex]T=pmt\\times12\\times t[\/latex]. To calculate this, the payment must be found. Using the information above, [latex]P = $225,879[\/latex], [latex]r = 0.0491[\/latex] and [latex]t = 15[\/latex]. Substituting those values into the formula [latex]pmt=\\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121}[\/latex] and calculating, we find the payment is:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{ll}<br \/>  PMT && = \\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121} \\\\<br \/>  && =\\frac{$$225,879\\times\\frac{0.0491}{12}\\times(1+\\frac{0.0491}{12})^{12\\times 15}}{(1+\\frac{0.0491}{12})^{12\\times 15}\u22121} \\\\<br \/>  && =\\frac{$225,879\\times(.004091\\overline{6})\\times(1.004091\\overline{6})^{180}}{(1.004091\\overline{6})^{180}\u22121} \\\\<br \/>  && =\\frac{$1927.439709}{1.085473955 } \\\\<br \/>  && = \\$1,775.67 \\\\<br \/>  \\end{array}[\/latex]<\/p>\n<p>\nUsing the mortgage payment of [latex]$1,775.67[\/latex] and [latex]t = 15[\/latex] years in the formula [latex]T=pmt\\times12\\times t[\/latex], the total that Arthur will pay for the mortgage is [latex]$319,618.80[\/latex].<br \/>\n<em>Note: Answers may vary slightly depending on how numbers were rounded.<\/em>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">Arthur buys a house. Their [latex]15[\/latex]-year mortgage comes to [latex]$225,879[\/latex] with [latex]4.91\\%[\/latex] interest. What was Arthur&#8217;s cost of financing?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160932\">Show Solution<\/button><\/p>\n<div id=\"q160932\" class=\"hidden-answer\" style=\"display: none\">We just found that the total that Arthur will pay for the [latex]$225,879[\/latex] mortgage is [latex]$319,618.80[\/latex]. (See previous example for the worked solution). <\/p>\n<p>Subtracting those we find the cost of financing [latex]CoF=T\u2212P = $319,618.80\u2212$225,879=$93,739.80[\/latex].<br \/>\n<em>Note: Answers may vary slightly depending on how numbers were rounded.<\/em>\n<\/div>\n<\/div>\n<\/section>\n<h3>Escrow Payments<\/h3>\n<div class=\"textbox shaded\">\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\n<p>An <strong>escrow account<\/strong> is a type of account that your mortgage lender sets up on your behalf when you close on your home. This account is used to pay certain property-related expenses on your behalf. The most common expenses that are paid out of an escrow account are property taxes and homeowners insurance. When you take out a mortgage, the lender typically divides the estimated annual cost of these expenses by [latex]12[\/latex] to determine a monthly amount. You then pay this amount as part of your monthly mortgage payment. The lender deposits these funds into the escrow account and then pays the expenses out of the account as they come due. This spreads out the cost of these large expenses into manageable monthly payments and ensures that these important bills are paid on time.<\/p>\n<\/div>\n<section class=\"textbox example\">Destiny decides to purchase a home, with a mortgage of [latex]$159,195.50[\/latex] at [latex]5.75\\%[\/latex] interest for [latex]30[\/latex] years. The assessed value of her home is [latex]$100,000[\/latex]. Her property taxes come to [latex]5.42\\%[\/latex] of her assessed value. Destiny also has to pay her home insurance every [latex]6[\/latex] months, and that comes to [latex]$843[\/latex] per [latex]6[\/latex] months. How much, including escrow, will Destiny pay per month?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160936\">Show Solution<\/button><\/p>\n<div id=\"q160936\" class=\"hidden-answer\" style=\"display: none\">\nUsing the payment function to find Destiny&#8217;s mortgage payments, [latex]pmt=\\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121}[\/latex], with [latex]P = $159,195.50[\/latex], [latex]r = 0.0575[\/latex] and [latex]t = 30[\/latex], her payments are:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{ll}<br \/>  PMT && = \\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121} \\\\<br \/>  && =\\frac{$159,195.50\\times\\frac{0.0575}{12}\\times(1+\\frac{0.0575}{12})^{12\\times 30}}{(1+\\frac{0.0575}{12})^{12\\times 30}\u22121} \\\\<br \/>  && = \\$929.02 \\\\<br \/>  \\end{array}[\/latex]<\/p>\n<p>Destiny also pays into escrow [latex]\\frac{1}{12}[\/latex] of her property taxes per month. Her property taxes are [latex]5.42\\%[\/latex] of the assessed value of [latex]$100,000[\/latex], which comes to [latex]0.0542\\times$100,000=$5,420[\/latex]. This is an annual tax, so she pays [latex]\\frac{1}{12}[\/latex] of that each month, or [latex]$451.67[\/latex]. Destiny&#8217;s home insurance is [latex]$843[\/latex] per [latex]6[\/latex] months, so each month she pays [latex]$140.50[\/latex] for insurance. <\/p>\n<p>Adding these together, her monthly payment is [latex]$929.02+$451.67+$140.50=$1,521.19[\/latex]. This is quite a bit more than the [latex]$929.02[\/latex] for the principal and interest.<\/p><\/div>\n<\/div>\n<\/section>\n<h2>Reading and Interpreting Amortization Tables<\/h2>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=10356039&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=E6amrtgENwY&amp;video_target=tpm-plugin-74xo56sx-E6amrtgENwY\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Amortization+Schedule+Explained.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cAmortization Schedule Explained\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<section class=\"textbox example\">Below is a portion of an amortization table for a [latex]30[\/latex]-year, [latex]$228,320[\/latex] mortgage. Use that table to answer the following questions.<\/p>\n<div style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4387\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/08161650\/CS_Photo_06_12_003.png\" alt=\"A spreadsheet labeled as amortization schedule calculator. The sheet calculates the repayment for the loan amount of $228,320.00 for an interest rate of 6.10 percent annually and the monthly payment is $1383.61 over 30 years. The factors include calculations such as month, payment, principal, interest, total, and interest and balance.\" width=\"603\" height=\"720\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/08161650\/CS_Photo_06_12_003.png 603w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/08161650\/CS_Photo_06_12_003-251x300.png 251w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/08161650\/CS_Photo_06_12_003-65x78.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/08161650\/CS_Photo_06_12_003-225x269.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/08161650\/CS_Photo_06_12_003-350x418.png 350w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/div>\n<p>&nbsp;<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li>What is the interest rate?<\/li>\n<li>How much are the payments?<\/li>\n<li>How much of payment [latex]235[\/latex] goes to principal?<\/li>\n<li>How much of payment [latex]215[\/latex] goes to interest?<\/li>\n<li>What\u2019s the remaining balance on the mortgage after payment [latex]227[\/latex]?<\/li>\n<li>At what payment does the amount that is applied to mortgage finally exceed the amount applied to interest?<\/li>\n<\/ol>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160934\">Show Solution<\/button><\/p>\n<div id=\"q160934\" class=\"hidden-answer\" style=\"display: none\">\n<ol style=\"list-style-type: decimal;\">\n<li>Reading at the top of the table, we see the interest rate is [latex]6.1\\%[\/latex].<\/li>\n<li>Reading from the top of the table or from the column labeled Payment, we see the payments are [latex]$1,383.61[\/latex] per month.<\/li>\n<li>In the row for payment [latex]235[\/latex], we see that the amount that goes to principal is [latex]$730.38[\/latex].<\/li>\n<li>In the row for payment [latex]215[\/latex], we see that the amount that goes to interest is [latex]$723.66[\/latex].<\/li>\n<li>In the row for payment [latex]227[\/latex], we see the remaining balance is [latex]$133,513.05[\/latex].<\/li>\n<li>Payment [latex]225[\/latex].<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n","protected":false},"author":15,"menu_order":24,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":4885,"module-header":"fresh_take","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4106"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":33,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4106\/revisions"}],"predecessor-version":[{"id":15410,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4106\/revisions\/15410"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/4885"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4106\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=4106"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=4106"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=4106"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=4106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}