Buying a House Project

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Texas A&M University, Commerce *

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1332

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Mathematics

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Feb 20, 2024

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Finance Chapter Project – “Buying A House” Name: Raven Wilson MATH 1332, College Mathematics Due: May 3, 2023 You are thinking about buying a house. To determine if this is feasible, you need to perform some calculations. Make sure to show all of your work, especially how the formulas are set up. You need to write something down for every part of each question. 1) Use the first three pages as a coversheet, and attach it to your project. Please do not write in the blanks beside the numbers. Make sure your name is on the top of the page. You need to save for a down payment. To find out how much you can save, you need to gather some income and savings information. / 3 2a) What is your gross annual income ? Every year, the U.S. Department of Housing and Urban Development (HUD) publishes the median family incomes (MFI) for various areas around the country. A chart with the latest HUD figures is located in D2L. Let’s assume that you have graduated and you have just landed a really good job. However, since you have little to no experience, your income may be lower than average, so let’s choose 80% Median Income. Pick your family size and use the income listed in the chart for the city/county where your future home is located. (Remember, if you pick a larger family size, you will need to choose a larger house to accommodate your family, so don’t just pick a family size because it has a higher income figure). Make sure to indicate your family size. You can also visit the HUD webpage at: https://www.huduser.gov/portal/datasets/il/il2018/select_Geography.odn / 3 2b) You need to calculate your net annual income . To keep things simple, we will say that taxes will be 25% of your gross income. So, Gross Income – (0.25  Gross Income) = Net Annual Income. / 3 2c) Suppose you decide to save 10% of your net monthly income . Find this amount. / 6 2d) If you invest this money in an account that compounds monthly with an APR of 2.5%, how much will you have saved i) after 1 year? ii) after 3 years? Before you buy a house, you need to determine what you can afford. / 4 3) The bank will not approve your mortgage loan if your monthly payment is greater than 28% of your gross monthly income . Find the maximum amount you can pay each month for your mortgage. Give a calculation to show that you can afford your mortgage. Now we get to the fun part. Happy house hunting! / 6 4) Find a house on the market. Remember that you need to have enough space for the entire family (that does not mean that every child must have his/her own room, but you can’t put grandma in with the kids! Just be reasonable.) Print or cut out the advertisement to attach to your project.

MATH 1332 Chapter 4 Project, “Buying a House” Page 2 / 3 5) Determine your down payment. For this project, select an amount that is 10% of the price of the home. / 3 6) Did your savings plan save enough for the down payment after 3 years? If not, then decide how you will adjust your savings plan either by extending the time you are saving or by increasing the amount each month to ensure you have enough for the down payment. / 4 7) How much of the house must be financed, i.e., after you make your down payment (see #5), how much of the cost of the house is still unpaid? This is your loan amount. / 6 8) Find the rates of two fixed mortgages, one with a term of 30 years, and one with a term of 15 years. Some lenders quote two different rates. Choose the rate labeled APR. Once you have found your rates, print out documentation of where you found your rates to attach to your project. Circle, highlight, or otherwise indicate the rate you choose. (Note: Rates on some websites change daily. Print out your documentation on the same day you choose the rate to make your calculations.) 9) For the loan with the 30 year term, find the following: / 6 9a) Calculate the monthly payment. (Show your work. You may NOT use an online mortgage calculator. This applies to #10a as well!) / 4 9b) Calculate the total amount paid for the loan. / 4 9c) Calculate the total interest paid for the loan. 10) For the loan with the 15 year term, find the following: / 6 10a) Calculate the monthly payment. / 4 10b) Calculate the total amount paid for the loan. / 4 10c) Calculate the total interest paid for the loan. BUT…the mortgage is not the only monthly cost you need to consider. You will also have to pay property taxes and homeowner’s insurance for your house. / 5 11) The property taxes should be stated on the real estate listing of the house. If not, try googling your property address to find another listing for the same property, or you can try calling the realtor. Divide the amount of property taxes by 12 to get your monthly tax payment. / 5 12) There are a number of things, such as size, age, number of stories, and location that can affect the cost of homeowner’s insurance, but valuation of the home for insurance purposes usually runs between $80 - $100 per square foot. To calculate a rough estimate, divide the purchase price (not the loan amount!) of the home by 1000 and multiply by $4. This gives you the annual premium. Divide by 12 to get your monthly insurance payment.

Raven Wilson Math 1332 CWID: 50101315 / 4 13a) What is the total monthly payment on the 30 year loan, including taxes and insurance? / 4 13b) Is the monthly payment on the loan with the 30 year term within your budget? If not, adjust your down payment, or find a cheaper house. If you have to adjust your down payment, determine how you will adjust your savings plan. If you need a cheaper house, print out the advertisement for the new house and calculate the new monthly payment. / 4 14a) What is the total monthly payment on the 15 year loan, including taxes and insurance? / 4 14b) Is the monthly payment on the loan with the 15 year term within your budget? If not, adjust your down payment, find a cheaper house, or choose the 30 year term. If you choose to adjust your down payment or find another house, then adjust your savings plan or find the new monthly payment, respectively. / 5 15) Write a paragraph where you determine which loan is better for your financial position. Explain your reasons for making your decision. You should address each of the following points. Which monthly payment will be easier to make? Which loan costs less in the long run? Which loan will allow you to get the better house? NOTE: Up to 10 points may be deducted for work that is messy, disorganized, or difficult to read. Your project should contain: 1) This coversheet 2) Documentation showing where you found your interest rates. 3) Documentation showing the details of the house(s) you are looking to buy. 4) Your work showing all of your calculations, including the formulas used to calculate each amount. Write down each formula you use and then show the formula with all of the variables filled in with the appropriate values. This should also contain your paragraph about your decision. REMEMBER TO READ ALL INSTRUCTIONS CAREFULLY. IF YOU HAVE ANY QUESTIONS, OR SOMETHING IS NOT CLEAR TO YOU, ASK!

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Raven Wilson Math 1332 CWID: 50101315 Buying A House Project 2a .) My family of 5 is made up of my husband and I, and three children. Two are girls (6 & 1) and a boy who is 10 years old. We are blessed to have a gross annual income of $66,700. My future home will be in Greenville, TX located inside Hunt County. 2b .) To calculate my net annual income, I’m going to use the formula of: Gross income – (0.25 x Gross Income) = Net Income $66,700 – (0.25 x 66,700) = $50,025 2c.) Saving 10% of my net monthly income would be: Net income x .10 = 10% of net monthly income $5,002.50 x .10 = $526.61 2d.) Investing $526.61 in an account with an APR of 2.5% after one year would save me: i) 10% of net monthly income x (1 + interest rate/12 x 12 months in 1 yr) $526.61 x (1 + 0.025/12 x 12) = $551.97 ii) After 3 years of interest, my investment will grow to: 10% of net monthly income x (1 + interest rate/12 x 36 months in 3 yrs) $5,002.50 x (1 + 0.025/12 x 36) = $602.63 3 .) I’m calculating an agreeable amount that should be approved for my monthly mortgage payment. I’m using the formula: Calculate 28% of $5,002.50 0.26 x $5,002.50 = $1,400.70 $1,400.70 is the maximum amount I can pay each month for my mortgage. If my loan amount is around $150,000, 20% down with a small interest rate of 4% on a 30-year loan term, my monthly payment would be $716.12. I could afford to buy a home with a higher loan amount. 4 .) I found a home located in Greenville, TX attached to this project. 5 .) The total price of the home is $189,900, and the down payment of 10% would be: $189,900 x 0.1 = $18.990 6.) My savings plan did not save enough for the down payment after 3 years. To adjust my savings plan I am going to extend the time I am saving each month to make sure I have the down payment. I will calculate the time frame by another three years. 7 .) After the down payment is paid, the remaining amount of the home that was financed is: $170,910. 8.) I found my two fixed mortgages online on nerdwallet.com. There on the website I found quotes for my inquiry about my home and attached those documents to my project.

Raven Wilson Math 1332 CWID: 50101315 9a .) The monthly payment for the fixed 30-year mortgage is: (Price of home x monthly interest rate) / (1 – (1+monthly interest rate) ^ (total number of payments) ($189,900 x 0.00527) / (2=0.00527) ^ (-360) = $1,180.69 monthly for 30yr fixed mortgage 9b .) To determine how much was paid for the loan, I calculated the monthly payment x total number of payments. MP (m x p) $1,180.69(12 x 30) $1,180.69 x 360 = $425,048.40 9c .) To calculate the total interest paid, I subtracted the initial loan amount from the total amount paid over the life of the loan. $425,052.40 - $189,900 = $235,152.40 The total interest paid is $235,152.40. 10a.) Calculate the monthly payment: (Price of home x monthly interest rate) / (1 – (1+monthly interest rate) ^ (total number of payments) ($189,900 x 0.00447917) / (1-(1+0.00447917) ^ (-180) Monthly Payment = $1,522.05 10b.) When determining how much was paid for the loan, I calculated the monthly payment times the total number of payments: MP (m x p) $1,180.69(12 x 15) $1,180.69 x 180 = $87,170.00 10c.) I used my calculations to get the total interest paid on the loan: Fixed monthly payments x total number of payments. $1,522.05 x 180 – $189,900 = $87,170.00 interest paid for the loan 11.) The property taxes on my future home are listed as: $4,106 (+ 27.1%) = $5,218.73 prop tax 12 .) (Purchase price / 1,000) x $4/12 (189,900 / 1,000) x $4 / 12 = $63.30 Insurance Estimate

Raven Wilson Math 1332 CWID: 50101315 13a.) To calculate the total monthly payment on the 30-year loan including taxes and insurance, I added the monthly principal and interest payment to the monthly property tax and insurance payments. Monthly property tax = (Purchase Price x Tax Rate) / 12 Monthly property tax = (189,900 x 0.015) 12 Monthly Property Tax = $237.38 Monthly insurance Payment = Annual Insurance Premium / 12 Monthly Insurance Payment = $760 / 12 Monthly Insurance Payment = $63.33 Total Monthly Payment = $860.89 + $237.38 + $63.33 Total Monthly Payment = $1,161.60 13b.) The monthly payment loan for the 30-year term is within my budget. 14a .) Monthly Property Tax Payment = (Purchase Price x Tax Rate) / 12 Monthly Property Tax Payment = ($189,900 x 0.015) / 12 Monthly Property Tax Payment = $237.38 Monthly Insurance Payment = Annual Insurance Premium / 12 Monthly Insurance Payment = $760 /12 Monthly Insurance Payment = $63.33 Total Monthly Payment = $1, 522 + $237.38 + $63.33 Total Monthly Payment = $1,822.76 14b.) The monthly payment of a 15-year term is not within my budget . I would opt to choose the 30-year term, because my monthly payment would be below my budget and feasible for me in the future moving forward. However, the 15-year term monthly payment isn’t quite bad considering the fact that it would have the time of the 30-year term with a added $400 dollars I won’t have per month. 15 .) Due to me having a family of 5 and a residual take home income of 50k I choose to pick my battles wisely and thoroughly. The loan that better fits my budget and future endeavors, is the 30-year fixed term which is well below my budget. Having a financially stable life is most important to me. The 30-year term monthly payment is around $300 dollars under my budget. This gives me more wiggle room for unexpected expenses. It is extremely vital that I prioritize what makes sense now and in the future. Life happens, and when it does, I will be proud to say I came prepared for whatever is thrown at me. Therefore, on a scale paying $1,161 for 30 years vs $1,822 for the 15-year term was a no brainer for me. Over time, I will be paying 4x more overall during the 30-year term than the 15-year term. However, his is the route I’d rather take. The 15- year term would allow me to get a much better house.

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