Business Math

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Business Math

Chapter 15: Mortgages

2Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

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.

Improvements include:

Water or sewage systems

Homes or commercial buildings

Any other type of structure


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.

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.

Key Terms


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.


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.


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.)


Use a per-$1,000 monthly payment table

Monthly mortgage payment

is equal to

Amount financed x table value

$1,000


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.


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.


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


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.


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


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


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.


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.


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


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


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.


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.


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


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.


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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