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Thinking Mathematically

Thinking Mathematically. The Cost of Home Ownership. Terminology. Mortgage broker - offers to find you a mortgage lender willing to make you a loan. Fixed rate mortgage - have the same monthly payment during the entire time of the loan

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Thinking Mathematically

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  1. Thinking Mathematically The Cost of Home Ownership

  2. Terminology • Mortgage broker- offers to find you a mortgage lender willing to make you a loan. • Fixed rate mortgage - have the same monthly payment during the entire time of the loan • Variable rate mortgage - have payment amounts that change from time to time depending on changes in the interest rate.

  3. Example Computing the Total Cost of Interest over the Life of a Fixed-Rate Mortgage The price of a home is $195,000. The bank requires a 10% down payment and two points at the time of closing. The cost of the home is financed with a 30-year fixed rate mortgage at 7.5% • Find the required down payment. • Find the amount of the mortgage. • How much must be paid for the two points at closing? • Find the monthly payment (excluding escrowed taxes and insurance). • Find the total cost of interest over 30 years.

  4. Solution a. The required down payment is 10% of $195,000 or 0.10  $195,000 = $19,500 b. The amount of the mortgage is the difference between the price of the home and the down payment. = $195,000 - $19,500 = $175,500

  5. Solution c. To find the cost of two points on a mortgage of $175,500, find 2% of $175,500. 0.02  $175,500 = $3510 The down payment ($19,500) is paid to the seller and the cost of two points ($3510) is paid to the lending institution.

  6. Solution d. We need to find the monthly mortgage payment. To do so we will use a monthly payment table. For a mortgage of 30 years at 7.5% the monthly payment per $1000 is $6.99. We can multiply this amount, $6.99, by the number of thousands of dollars in the mortgage amount to find the monthly payment for the entire mortgage amount. We divide the mortgage amount $175,500 by $1000 to find the number of thousands of dollars in the mortgage amount.

  7. Solution part d cont. $175,5000/$1000 = 175.5 The monthly mortgage payment is found by multiplying the number of thousands of dollars in the mortgage, 175.5, by the amount in the table, $6.99. 175.5  $6.99 = $1226.75 The monthly mortgage payment for principal and interest is $1226.75.

  8. Solution e. The total cost of interest over 30 years is equal to the difference between the total of all monthly payments and the amount of the mortgage. The total of all monthly payments is equal to the amount of the monthly payment multiplied by the number of payments. We found the amount of the monthly payment in (d): $1226.75. The number of payments is equal to the number of months in a year, 12, multiplied by the number of years in the mortgage, 30: 12  30 = 360. Thus the total of all monthly payments = $1226.75  360.

  9. Solution part e cont. Now we can calculate the interest over 30 years. = $1226.75  360 - $175,500 = $441,630 - $175,500 = $266,130 The total cost of interest over 30 years is $266,130.

  10. Thinking Mathematically The Cost of Home Ownership

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