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 March 17th, 2011, 06:47 PM #1 Newbie   Joined: Mar 2011 Posts: 2 Thanks: 0 Mortgage Assignment In this project we will examine a home loan or mortgage. Assume that you have found a home for sale and have agreed to a purchase price of $200,000. Down Payment: You are going to make a 10% down payment on the house. Determine the amount of your down payment and the balance to finance. Down Payment______________ Mortgage Amount__________________ Interest Rates: Assume that a lending institution will loan you the money you need at: 6.5% for a 15 year mortgage and at 7% for a 30 year mortgage Monthly Payment: Calculate the monthly payment for both loans (rounding up by the nearest cent) by using the following formula: PMT= P x (APR/n) / 1-(1+APR/n)^-ny 15-yr Monthly Payment_____________________ 30-yr Monthly Payment___________________________ Amortization Schedule: In order to summarize all the information regarding the amortization of a loan, construct a schedule that keeps track of the payment number, the principal paid, the interest, and the unpaid balance. A spreadsheet program is an excellent tool to develop an amortization schedule. We can use a free amortization spreadsheet on the web. The web address is: http://mortgage-x.com/calculators/extra ... ulator.asp. Enter the amount of the loan, i.e. the selling price minus the down payment, the interest rate, and the appropriate number of years. Check the box to show the schedule. Amortization Schedule monthly payment for a 30 year mortgage _____________ (Note: if this is more than 2 or 3 cents different from your calculation, check your numbers!) Total interest paid over 30 years____________ Total amount paid _____________ Notice that the amount of the payment that goes towards the principal and the amount that goes towards the interest are not constant. What do you observe about each of these values? Number of first payment when more of payment goes toward principal than interest _________ As already mentioned, these payments are for principal and interest only. You will also have monthly payments for home insurance and property taxes. In addition, it is helpful to have money left over for those little luxuries like electricity, running water, and food. As a wise home owner, you decide that your monthly principal and interest payment should not exceed 35% of your monthly take-home pay. What minimum monthly take-home pay should you have in order to meet this goal? Show your work for making this calculation. Minimum monthly take home pay = ________________________. Show work here It is also important to note that your net or take-home pay (after taxes) is less than your gross pay (before taxes). Assuming that your net pay is 73% of your gross pay, what minimum gross annual salary will you need to make to have the monthly net salary stated above? Show your work for making this calculation. Minimum gross annual salary = __________________________ Part II: Selling the House Let's suppose that after living in the house for 10 years, you want to sell. The economy experiences ups and downs, but in general the value of real estate increases over time. To calculate the value of an investment such as real estate, we use continuously compounded interest. Find the value of the home 10 years after purchase assuming a continuous interest rate of 4%. Use the full purchase price as the principal. Show your work. Value of home 10 years after purchase _______________________ Show work here. Show work here. Assuming that you can sell the house for this amount, use the following information to calculate your gains or losses: Selling price of your house ___________________ Original down payment ________________ Mortgage paid over the ten years _______________ The principal balance on your loan after ten years __________________ Do you gain or lose money over the 10 years? How much? Show your amounts and summarize your results: Part III: 15 year Mortgage Using the same purchase price and down payment, we will investigate a 15 year mortgage. Monthly Payment: Calculate the monthly payment for a 15 year loan (rounding up to the nearest cent) by using the following formula. Show your work! [PMT is the monthly loan payment, P is the mortgage amount, r is the annual percent rate for the loan in decimal, and Y is the number of years to pay off the loan.] For the 15 year loan use an annual interest rate of 4.735%. Monthly Payment for a 15 year mortgage = _____________ Show work here. ( ) ( ) 1 2 1 2 1 2 1 1 r Y r P PM T ? = ? + Use the amortization spreadsheet on the web again, this time entering the interest rate and number of payments for a 15 year loan. Amortization Schedule monthly payment for a 15 year mortgage _____________ (Note: if this is more than 2 or 3 cents different from your calculation, check your numbers!) Total interest paid over 15 years____________ Total amount paid_____________ Number of first payment when more of payment goes toward principal than interest _________ Suppose you paid an additional$100 towards the principal each month. How long would it take to pay off the loan with this additional payment and how will this affect the total amount of interest paid on the loan? [If you are making extra payments towards the principal, include it in the monthly payment and leave the number of payments box blank.] Length of time to pay off loan with additional payments of $100 per month________________ Total interest paid over the life of the loan with additional$100 monthly payments___________ Total amount paid with additional \$100 monthly payments_____________ Compare this total amount paid to the total amount paid without extra monthly payments. How much more or less would you spend if you made the extra principal payments?
 March 17th, 2011, 07:50 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Re: Mortgage Assignment Can you calculate the down payment?

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