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Business Math

Business Math. Chapter 15: Mortgages. 15.1 Mortgage Payments. Find the monthly mortgage payment using a table Find the total interest on a mortgage. Key Terms. A home is a type of “real” property. Real estate or real property is land plus any permanent improvements to the land.

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Business Math

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  1. Business Math Chapter 15: Mortgages

  2. 15.1 Mortgage Payments • Find the monthly mortgage payment using a table • Find the total interest on a mortgage

  3. Key Terms • A home is a type of “real” property. Real estateor real property is land plus any permanent improvements to the land. • Improvements include: • Water or sewage systems • Homes or commercial buildings • Any other type of structure

  4. Key Terms • Mortgage: a loan in which real property is used to secure the debt. • Collateral: the property that is held as security on a mortgage. • Equity: the difference between the expected selling price and the balance owed on the property.

  5. Key Terms • Market value: the expected selling price of a property. • First mortgage: the primary mortgage on a property. • Conventional mortgage: a mortgage that is not insured by a government program.

  6. Conventional mortgages • Two types include: • Fixed-rate mortgage: the rate of interest on the loan remains the same for the life of the mortgage. • Adjustable-rate mortgage: the rate of interest may fluctuate during the life of the loan depending on the prime lending rate of most banks.

  7. Mortgage payments • 15 - year and 30 - year loans are the most common. • Payments can be made monthly or on a biweekly plan, resulting in 26 payments. • The biweekly plan builds equity more quickly than the monthly plan. • An equity line of credit, or second mortgage, allows a homeowner to borrow against the equity in the home. It is in addition to the first mortgage.

  8. 15.1.1 Find the monthly mortgage payment using a table • The repayment of a loan in equal installments that are applied to principal and interest over a period of time is called the amortization of a loan. • To calculate the monthly mortgage payment, it is customary to use a table. (See Figure 15.1 in your text.)

  9. Use a per-$1,000 monthly payment table Monthly mortgage payment is equal to Amount financed x table value $1,000

  10. Look at this example • A homebuyer is purchasing a house for $87,000. The bank has approved her loan application for a 30-year fixed-rate loan at 7% annual interest. If she makes a 20% down payment, what is the monthly payment? • Calculate the down payment: $87,000 x 0.20. • It is $17,400. • The balance to be financed would be $69,600. • Divide $69,600 by $1,000 = 69.6.

  11. Example (continued) • Using Table 15-1, find the factor for financing a loan for 30 years at 7%. • The factor is 6.65 • Multiply this factor (6.65) by number of thousands (69.6). • The result is $462.84 • The monthly payment of $462.84 includes the principal and the interest.

  12. Try this example. • Joan Williams has been approved for a 30-year fixed-rate loan at 6.5%. The home that she is purchasing costs $140,000; she is going to put 20% down. • Calculate her monthly payment including principal and interest using Table 15-1. • $707.84

  13. 15.1.2 Find the total interest on a mortgage • Find the total number of payments: multiply the number of payments by the amount of the payment. • Subtract the amount financed from the total of the payments.

  14. Look at this example • In the example on Slide 11, the monthly payment of the principal and interest is $462.84. The buyer has a 30-year fixed mortgage. • Total interest = number of payments x amount of payment – amount financed. • TI = 30 x 12 x $462.84 - $69,600 • TI = $166,622.40 - $69,600 • The total interest on this loan is $97,022.40

  15. Try this example • Joan Williams’ monthly mortgage payment is $707.84. Find the total interest on her 30-year mortgage. The amount financed is $112,000. Find the total interest on the mortgage. • $142,822.40

  16. Key Terms • Other costs involved in securing a mortgage include: points, attorney fees, and sales commissions among others. These are called closing costs,and are paid when the loan is made. • Points: a one-time payment to the lender that is a percent of the total loan. • Escrow: an account for holding the part of a monthly payment that is used to pay taxes and insurance.

  17. PITI • The adjusted monthly payment that includes the principal, interest, taxes and insurance is abbreviated “PITI.” • The monthly mortgage payment that the borrower will make will include all four elements.

  18. Look at this example. • Our home buyer (from Slides 11 and 14) has a monthly payment of principal and interest of $462.84. If her annual insurance premium is $923 and the property taxes are $950, find the adjusted monthly payment that includes PITI. • $923 + $950 = $1,873 ÷ 12 = $156.08 • Add the above amount to the monthly principal and interest payment of $462.84. • The adjusted monthly payment = $618.92

  19. Try this example • The other homebuyer has a monthly payment of principal and interest of $707.84. If her annual insurance premium is $1,200 and her property taxes are $1,500, what would the adjusted monthly payment be? • $932.84

  20. 15.2 Amortization schedules To prepare an amortization schedule of a mortgage: Step 1: For the first month, • Find the interest portion of the first monthly payment = original principal x monthly interest rate. • Find the principal portion of the monthly payment = monthly payment – interest portion of the first monthly payment. • Find the end of month principal = original principal –principal portion of the first monthly payment.

  21. For each remaining month in turn: • Step 2 (for each remaining month) • Find the interest portion of the monthly payment = previous end-of-month principal x monthly interest rate. • Find the principal portion of the monthly payment = monthly payment – interest portion of the monthly payment. • Find the end-of-month principal = previous end-of month principal – principal portion of the monthly payment.

  22. Look at this example • From the first home buyer example, Interest = original principal x monthly rate • Interest = $69,600 x 0.07 /12 • Interest = $406.00 • Principal portion of the monthly payment =$462.84 - $406 = $56.84 • End-of-month principal =$69,600 - $56.84 = $69,543.16

  23. Example (continued) Second month • Interest portion = $69,543.16 x 0.07 / 12 • Interest portion = $405.67 • Principal portion of monthly payment =$462.84 - $405.67 = $57.17 • End of month principal = $69,543.16 - $57.17 = $69,485.99 • Follow the same steps for subsequent months.

  24. Try this example • Joan Williams, the other homebuyer, has a monthly mortgage payment of $707.84; an original loan amount of $112,000 and a 6.5% interest rate. Calculate the first two months of an amortization schedule. • First end-of-month principal =$111,898.82 • Second end-of-month principal =$111,797.09

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