Some people will purchase a home or condo with cash, but the majority of people will apply for a mortgage<\/strong>.<\/p>\r\n A mortgage is a long-term loan and the property itself is the security. The loan provider decides the minimum down payment (with your input), the payment schedule, the duration of the loan, whether the loan can be assumed by another party, and the penalty for late payments. The title of the home, while under mortgage, belongs to the bank.<\/p>\r\n A mortgage <\/strong>is a type of loan that individuals or businesses take out to purchase real estate. This loan is secured by the property itself, meaning the lender has the right to take possession of the property if the borrower fails to make the required payments.<\/p>\r\n<\/div>\r\n<\/section>\r\n Mortgage loans are typically paid back over a long period, commonly [latex]15[\/latex] or [latex]30[\/latex] years, in a series of regular payments that usually cover both the principal (the original amount borrowed) and the interest (the cost of borrowing).<\/p>\r\n A mortgage payment is typically made up of four parts: the principal, the interest, taxes, and insurance. This is often abbreviated as PITI.<\/p>\r\n Private Mortgage Insurance (PMI)<\/strong><\/p>\r\n When you purchase a home, you will have to pay a down payment. This means you have money tied to the property, which lenders believe makes you less likely to walk away from a property. The amount of the down payment will be decided between you and the mortgage company.<\/p>\r\n However, if your down payment is less than [latex]20\\%[\/latex] of the property value, you will be required to pay private mortgage insurance (PMI). This is insurance you pay for so that the mortgage company is protected if you default on the loan. It often comes to between [latex]0.5\\%[\/latex] and [latex]2.25\\%[\/latex] of the original loan amount. It increases your monthly payment. Once you reach [latex]20\\%[\/latex] of the loan value, you can request that the PMI be dropped. Even if you do not request cancelling the PMI, it will eventually and automatically be dropped.<\/p>\r\n<\/section>\r\n To manage your mortgage effectively, it's vital to understand the mechanics of your monthly payments. The calculation involves the [pb_glossary id=\"14046\"]Annual Percentage Rate (APR)[\/pb_glossary], which serves as the basis for the yearly interest.<\/p>\r\n The payment, [latex]pmt[\/latex], per month to pay down a mortgage with beginning principal [latex]P[\/latex] is<\/p>\r\n <\/p>\r\n <\/p>\r\n where [latex]r[\/latex] is the annual interest rate in decimal form and [latex]t[\/latex] is the number of years of the payment.<\/p>\r\n Note, payment to lenders is always rounded up to the next penny.<\/em><\/p>\r\n<\/div>\r\n<\/section>\r\n [latex]\\begin{array}{ll} <\/p>\r\n You can view the transcript for \u201cHow To Calculate Your Mortgage Payment\u201d here (opens in new window).<\/a><\/p>\r\n You can view the transcript for \u201cHow To Calculate Your Monthly Mortgage Payment Given The Principal, Interest Rate, & Loan Period\u201d here (opens in new window).<\/a><\/p>\r\n You can view the transcript for \u201cHow To Calculate A Mortgage Payment Amount - Mortgage Payments Explained With Formula\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n Understanding the full cost of a loan over its duration is crucial for financial planning. To find the total amount of your payments over the life of the loan, multiply your monthly payments by the number of payments. This can be useful information, but not too many people reach the end of their mortgage since most tend to move before the mortgage is paid off.<\/p>\r\n 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<\/div>\r\n<\/section>\r\n [latex]\\begin{array}{ll} To fully grasp the financial implications of a mortgage, it's essential to understand the concept of financing cost. This cost is the difference between the total amount paid back over the life of the mortgage and the original loan amount, or principal.<\/p>\r\n 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>\r\n We're aware that mortgage payments consist of four parts, commonly abbreviated as PITI. Our examples so far have focused on the principal and interest. Through an escrow account<\/strong>, the 'T' and 'I'\u2014taxes and insurance\u2014are also collected to ensure these obligations are fulfilled without requiring separate payments.\u00a0<\/p>\r\n An 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.<\/p>\r\n<\/div>\r\n<\/section>\r\n Here's how escrow accounts typically work:<\/p>\r\n [latex]\\begin{array}{ll} Some people will purchase a home or condo with cash, but the majority of people will apply for a mortgage<\/strong>.<\/p>\n A mortgage is a long-term loan and the property itself is the security. The loan provider decides the minimum down payment (with your input), the payment schedule, the duration of the loan, whether the loan can be assumed by another party, and the penalty for late payments. The title of the home, while under mortgage, belongs to the bank.<\/p>\n A mortgage <\/strong>is a type of loan that individuals or businesses take out to purchase real estate. This loan is secured by the property itself, meaning the lender has the right to take possession of the property if the borrower fails to make the required payments.<\/p>\n<\/div>\n<\/section>\n Mortgage loans are typically paid back over a long period, commonly [latex]15[\/latex] or [latex]30[\/latex] years, in a series of regular payments that usually cover both the principal (the original amount borrowed) and the interest (the cost of borrowing).<\/p>\n A mortgage payment is typically made up of four parts: the principal, the interest, taxes, and insurance. This is often abbreviated as PITI.<\/p>\n Private Mortgage Insurance (PMI)<\/strong><\/p>\n When you purchase a home, you will have to pay a down payment. This means you have money tied to the property, which lenders believe makes you less likely to walk away from a property. The amount of the down payment will be decided between you and the mortgage company.<\/p>\n However, if your down payment is less than [latex]20\\%[\/latex] of the property value, you will be required to pay private mortgage insurance (PMI). This is insurance you pay for so that the mortgage company is protected if you default on the loan. It often comes to between [latex]0.5\\%[\/latex] and [latex]2.25\\%[\/latex] of the original loan amount. It increases your monthly payment. Once you reach [latex]20\\%[\/latex] of the loan value, you can request that the PMI be dropped. Even if you do not request cancelling the PMI, it will eventually and automatically be dropped.<\/p>\n<\/section>\n To manage your mortgage effectively, it’s vital to understand the mechanics of your monthly payments. The calculation involves the Annual Percentage Rate (APR)<\/a>, which serves as the basis for the yearly interest.<\/p>\n The payment, [latex]pmt[\/latex], per month to pay down a mortgage with beginning principal [latex]P[\/latex] is<\/p>\n <\/p>\n <\/p>\n where [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 Note, payment to lenders is always rounded up to the next penny.<\/em><\/p>\n<\/div>\n<\/section>\nmortgage<\/h3>\r\n
Monthly Mortgage Payments<\/h3>\r\n
\r\n\t
mortgage payment formula<\/h3>\r\n
\r\n[reveal-answer q=\"160930\"]Show Solution[\/reveal-answer]
\r\n[hidden-answer a=\"160930\"]
\r\nUsing the information above, [latex]P = $132,650[\/latex], [latex]r = 0.048[\/latex] and [latex]t = 30[\/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\r\n
\r\nPMT && = \\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121} \\\\
\r\n&& =\\frac{$132,650\\times\\frac{0.048}{12}\\times(1+\\frac{0.048}{12})^{12\\times 30}}{(1+\\frac{0.048}{12})^{12\\times 30}\u22121} \\\\
\r\n&& =\\frac{$132,650\\times(.004)\\times(1.004)^{360}}{(1.004)^{360}\u22121} \\\\
\r\n&& =\\frac{$2,233.07781448}{3.20858992551} \\\\
\r\n&& = \\$695.97 \\\\
\r\n\\end{array}[\/latex]<\/p>\r\n
\r\nHis mortgage payment is [latex]$695.97[\/latex].
\r\nNote: Answers may vary slightly depending on how numbers were rounded.<\/em>
\r\n[\/hidden-answer]<\/section>\r\n
\r\n[videooption displayName=\"How To Calculate Your Mortgage Payment\" value=\"\/\/plugin.3playmedia.com\/show?mf=12452605&p3sdk_version=1.10.1&p=20361&pt=375&video_id=-5cw1xc8pTw&video_target=tpm-plugin-5crx2zmu--5cw1xc8pTw\"][videooption displayName=\"How To Calculate Your Monthly Mortgage Payment Given The Principal, Interest Rate, & Loan Period\" value=\"\/\/plugin.3playmedia.com\/show?mf=12452606&p3sdk_version=1.10.1&p=20361&pt=375&video_id=6bLg_Ex0A-4&video_target=tpm-plugin-eufiaxjf-6bLg_Ex0A-4\"] [videooption displayName=\"How To Calculate A Mortgage Payment Amount - Mortgage Payments Explained With Formula\" value=\"https:\/\/youtu.be\/Wzcn2I_6OCs\"]
\r\n[\/videopicker]\r\n\r\ntotal payment formula<\/h3>\r\n
\r\n[reveal-answer q=\"160931\"]Show Solution[\/reveal-answer]
\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 = $99,596[\/latex], [latex]r = 0.0535[\/latex] and [latex]t = 30[\/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\r\n
\r\nPMT && = \\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121} \\\\
\r\n&& =\\frac{$99,596\\times\\frac{0.0535}{12}\\times(1+\\frac{0.0535}{12})^{12\\times 30}}{(1+\\frac{0.0535}{12})^{12\\times 30}\u22121} \\\\
\r\n&& =\\frac{$99,596\\times(.004458\\overline{3})\\times(1.004458\\overline{3})^{360}}{(1.004458\\overline{3})^{360}\u22121} \\\\
\r\n&& =\\frac{$2,202.458911222}{3.9601341693} \\\\
\r\n&& = \\$556.16 \\\\
\r\n\\end{array}[\/latex]<\/p>\r\n
\r\nUsing the mortgage payment of [latex]$556.16[\/latex] and [latex]t = 30[\/latex] years in the formula [latex]T=pmt\\times12\\times t[\/latex], the total that Maya will pay for the mortgage is [latex]$200,217.60[\/latex].
\r\nNote: Answers may vary slightly depending on how numbers were rounded.<\/em>
\r\n[\/hidden-answer]<\/section>\r\ncost of financing<\/h3>\r\n
\r\n[reveal-answer q=\"160932\"]Show Solution[\/reveal-answer]
\r\n[hidden-answer a=\"160932\"]We just found that the total that Maya will pay for the [latex]$99,569[\/latex] mortgage is [latex]$200,217.60[\/latex]. (See previous example for the worked solution).
\r\n
\r\nSubtracting those we find the cost of financing [latex]CoF=T\u2212P = $200,217.60\u2212$99,596=$100,621.60[\/latex].
\r\nNote: Answers may vary slightly depending on how numbers were rounded.<\/em>
\r\n[\/hidden-answer]<\/section>\r\nEscrow Payments<\/h3>\r\n
escrow account<\/h3>\r\n
\r\n\t
\r\n[reveal-answer q=\"160936\"]Show Solution[\/reveal-answer]
\r\n[hidden-answer a=\"160936\"]
\r\nUsing the payment function to find Kai'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 = $108,450[\/latex], [latex]r = 0.06[\/latex] and [latex]t = 30[\/latex], their payments are:\r\n\r\n
\r\nPMT && = \\frac{P\\times\\frac{r}{12}\\times(1+\\frac{r}{12})^{12\\times t}}{(1+\\frac{r}{12})^{12\\times t}\u22121} \\\\
\r\n&& =\\frac{$108,450\\times\\frac{0.06}{12}\\times(1+\\frac{0.06}{12})^{12\\times 30}}{(1+\\frac{0.06}{12})^{12\\times 30}\u22121} \\\\
\r\n&& = \\$649.95 \\\\
\r\n\\end{array}[\/latex]<\/p>\r\n\r\n\r\nKai also pays into escrow [latex]\\frac{1}{12}[\/latex] of their property taxes per month. Their property taxes are [latex]5.7\\%[\/latex] of the assessed value of [latex]$75,600[\/latex], which comes to [latex]0.057\\times$75,600=$4309.20[\/latex]. This is an annual tax, so they pay [latex]\\frac{1}{12}[\/latex] of that each month, or [latex]$359.10[\/latex].
\r\n
\r\nKai's home insurance is [latex]$744[\/latex] per [latex]6[\/latex] months, so each month they pay [latex]$124.00[\/latex] for insurance.
\r\n
\r\nAdding these together, their monthly payment is [latex]$649.95+$359.10+$124.00=$1,133.05[\/latex].
\r\n
\r\nThis is quite a bit more than the [latex]$649.95[\/latex] for the principal and interest.[\/hidden-answer]<\/section>","rendered":"Understanding and Calculating Mortgage Payments<\/h2>\n
mortgage<\/h3>\n
Monthly Mortgage Payments<\/h3>\n
\n
mortgage payment formula<\/h3>\n