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Business Math Chapter 6 Notes

Section 6 – 1: Borrowing to Buy a Home

Definitions

Down payment – a cash payment or percentage of the total cost of a house paid at the time of purchase to the lender.

Mortgage loan – paper signed by a borrower that gives the lender the right to ownership of property if the borrower does not pay the principal or interest.

Principal – The amount of money borrowed on which interest needs to be paid.

Closing costs – fees and expenses paid to complete the transfer of ownership of a home.

*3% - 6% of purchase price.

Legal fees Recording fees Title insurance Loan application fees Appraisal/inspection fees

Mortgage loan = Purchase price – down payment.

Cash need to buy = Down payment + closing costs.

Ex 1

Buying $120,000 house. 15% down payment. 4% closing costs.

A. How much to borrow for a mortgage loan?

Down payment = $120,000 * .15 = $18,000

Mortgage loan = $120,000 – 18,000 = $102,000

B. How much “cash” needed at closing

Down payment: $18,000

Closing costs = $120,000 * .04 = $4,800

18,000 + 4,800 = $22,800

Two types of Mortgages

1. Fixed rate mortgage – same interest rate for the length of the loan.

2. Variable rate – rate could increase or decrease throughout the length of the loan.

Monthly payments = principal and interest

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*Use an Amortization Table to find a monthly payment.

Ex 2

Bought home for 95,000. $15,000 down payment. 20 year mortgage at 7%.

A. Monthly payments

80,000, 20 years, 7% = $620.24

B. Total interest paid over 20 years.

620.24 * 12 * 20 = $148,857.60

148,857.60 – 80,000 = $68,857.60

Pg. 214 11 – 23, 34 - 36

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6-1 Part Two

Definitions

Refinancing a Mortgage – Why?

To get a lower interest rate Will be charged closing costs and other fees.

Ex 1Current payment: $597Refinanced payment: $465Cost of new mortgage: $836 A. How much will you save in the first year?Old mortgage: 597 * 12 = $7,164New mortgage: 465 * 12 = 5,580 5,580 + 836 = $6,416

Savings: 7,164 – 6416 = $748

Ex 2Current payment: $982Refinance payment: $876Closing costs: $716Prepayment charge: $ 485

A. Savings in first yearCurrent: 982 * 12 = $11,784Refinanced: 876 * 12 = $10,51210,512 + 716 + 485 = $11,713

Savings: 11,784 – 11,713 = 71

B. Total savings after two years.Year two: 11,784 – 10,512 = $1,2721,272 + 71 = $1,343

C. After three years.1,272(2) + 71 = $2,615

Pg. 214 24 – 28

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Section 6 – 2 Renting or owning a home

Definitions

Depreciation – the loss in value of a property caused by aging and use. * 1 – 4 % per year.

Security Deposit – an amount of money given to guarantee a lease.

Ex 1

Buying $87,000 house

Estimated expenses during the first year.

Mortgage interest = $5,788Property tax = $1,904Insurance = $347Lost interest income = $1,140Depreciation = 2% of costMaintenance/Repairs = $900Utilities = $1,860Save on income tax = $1,050

A. Net cost of owning home in first year

Depreciation: $.02(87,000) = $1,740

5,788 + 1,904 + 347 +1140 + 1740 + 900 + 1860 = 13,679

13,679 – 1050 = $12,629

Ex 2

Rent apartment for one year.

$625 rent$700 security deposit$85 insurance$1,210 utilities

A. Cost of renting for a year.

Rent: 625 * 12 = 7,500

7,500 + 700 + 85 + 1210 = $9,495

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Comparing: Renting vs. Owning

Ex 3

House = $83,600

Buying

Loan interest,

Tax, insurance, maintenance = $9,100

Depreciation = $2,926

Lose $560 of interest on down payment

Save $1,600 on income tax

Rent

$785 rent (785 * 12 = 9,420)

Insurance $115

Utilities $1,150

Security deposit $200

A. Cost of buying house first year = $10,986

B. Cost of renting = $10,885

C. Is it cheaper to rent or buy?

$101 cheaper to rent

Pg. 221 (9 – 15, 24)

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Section 6 – 3 Property Tax

Definitions

Property tax – taxes on the value of real estate. *collected annually or semiannually

Assessed value – value put on property as a base for figuring amount of tax. * Usually less than market

value.

Decimal tax rate – tax rate at which property is to be taxed.

Decimal Tax Rate = Amount to be raised by property tax Total assessed valueEx 1

County budget $6,750,000

$650,000 raised from “other income.” The rest was from property tax.

Total assessed value of county’s property = $80,000,000

A. decimal tax rate

6,750,000 – 650,000 = 6,100,000

Decimal tax rate = 6,100,000 = .0762 80,000,000

Tax rates per $100 or per $1000

Ex 2

Tax rate $3.736 per 100

Assessed value $42,000

A. Amount of tax bill

42,000 = 420 units of $100

420 * 3.736 = $1,569.12

Ex 3

Tax rate $50.08 per $1,000

Assessed value $67,500

A. Tax bill $67,500 = 67.5 units of $1,000

67.5(50.08) = $3,380.40

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Tax rate in mills or cents per dollar

Mill = one tenth of a cent or one thousandth of a dollar

10 mills = 1 cent

1,000 mills = 1 dollar

Ex 4

Tax rate 52 mills per $1.00 of assessed value.

Assessed value: $38,400

52 mills/1,000 = $.052

38,400(.052) = $1,996.80

Pg. 227 7 - 24

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Section 6 – 4 Property Insurance

Definitions

Homeowners insurance – a policy that covers your home and protects you against other risks.

Building

Personal property

Personal liability

Premium – the money paid to an insurance company for property insurance.

Renters Policy – similar to homeowners insurance, but doesn’t cover the loss of the building or

apartment.

Ex 1

Insured a home for $61,000. Policy costs $.46 per $100.

A. Annual premium to the nearest dollar.

61,000/100 = 610 units of $100

610 (.46) = 280.60 = $281

Ex 2

Insure apartment’s contents for $25,000. Additional insurance for $3,000 of jewelry for an additional

$31. Live one block from the fire station.

A. Use chart on page 231 and find total premium for one year.

Chart = $165

165 + 31 = $196

Collecting on a claim

Deductible – amount you pay out of pocket before your claim will be covered.

Ex 3

How much will insurance pay for a loss of $10,200 if the property is insured for $18,000 with a $250

deductible?

10,200 – 250 = $9,950

Coinsurance policy – purchase insurance up to a state percent of value.

Amount Paid = Face value of policy * amount of loss Required amount of coinsurance

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Ex 4

80% coinsurance policy of $41,600. The home is worth $65,000 loss of $4,000.

.8 (65,000) = 52,000

41,600 * 4,000 = $3,20052,000

Pg. 234 15 - 29

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Section 6 – 5 Buying a Car

Definitions

MSRP (Manufacturer’s Suggested Retail Price), or sticker price. The price printed on a sticker pasted on the window of a new car. The sticker also lists the equipment on the car and mileage information.

Negotiation – where the buyer and seller of the vehicle come to an agreed price for the vehicle.

6 - 5 Check Understanding B, D, F Pg. 245 – 247

Section 6 – 6 Purchases and Lease

Definitions

Lease – a contract made between the company that owns the car (lessor) and the person given the right to use the car (lessee.)

Financing Car Purchases

Ex 1Buy used truck for $9,650. Paid $2,650 down payment. 36 monthly payments at $234.40.

a. How much did you actually pay for the truck?2,650 + 36(234.40) = $11,084.80

b. Finance charge11,084.80 – 9,650 = $1,434.80

Cost of Leasing – leasing a car similar to renting an apartment.

Lease contract includes: Lease price Down payment Residual value – expected value of car at end of lease period Interest rate Lease term – length of lease in months Security deposit – held by dealer in case of damage. Refundable. Loan fee Registration fee – license plates and title registration Mileage allowed – number of miles per year. Additional miles = charge.

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Ex 2Two year lease$528 monthly payment12,000 mile per year limit$.20 per mile charge for over mileageTotal miles = 30,850

a. How many miles over 30,850 – 24,000 = 6,850

b. Total cost of lease over the two years.528 (24) + 6,850 (.20) = $14,042

Comparing Leasing and Buying

Ex 3Car costs 18,500Leased Loan$435 per month $728 per month$500 down $3,100 down payment$11,000 residual

24 monthsa. Cost to lease then buy436(24) = 10,46410,464 + 500 + 11,000 = $21,964

b. Cost to buy with loan728(24) = 17,47217,472 + 3,100 = 20,572

c. Which is less expensive

*Buying by $1,392 less

6 - 6 Pg. 248 9 – 17

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Section 6 – 7 Depreciating a Car

Definitions

Resale value – market value – amount you would get when you sell the car.

Trade-in value – the amount you would get for your old car when buying a new car.

Depreciation – original cost – Trade-in or resale value.

*Can calculate “estimated average annual depreciation.”

Average Annual Depreciation = original – trade/resale value Number of yearsEx 1New car $19,500

Will be worth $9,800 in two years.

a. Total depreciation

19,500 – 9,800 = $9,700

b. Average annual depreciation

9,700/2 = $4,850

Rate of depreciation = Average annual depreciation Original cost

Ex 2

Sold car for $368. Bought it for $9,200, 12 years ago.

a. Annual rate of depreciation

9,200 – 368 = 8,832

8,832/12 = 736

736/9,200 = .08 = 8%

pg. 253 7 – 22

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Section 6 – 8 Cost of owning a car

Types of insurance

1. Bodily injury – covers your liability for injury to others.

2. Property damage – covers damage to other people’s property, including their vehicles.

3. Collision – covers damage to your own vehicle.

4. Comprehensive damage – covers damage or loss to your vehicle from fire, theft, vandalism, hail and

other causes.

Ex 1

Drives car to work:

Coverage

$25/50,000 bodily injury

$50,000 property damage

$250 deductible collision

$100 deductible comprehensive

a. Find premium

22.84 + 179.44 + 358.24 + 104.33 = $664.85

Cost of Operating Cars

Insurance Gas

Oil License

Tires Repairs

Parking fees (garage) Taxes

General maintenance Depreciation

Interest lost on down paymentEx 2

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Bought used car $12,480

Expenses

Gas/oil = 1,070

Repairs = 512

Insurance = 981

License plates = 83

Loss of interest = 561

Depreciation = 12%

a. Cost in first year.

Depreciation 1240 * .12 = 1497.60

Cost = 1497.60 + 1070 + 512 + 981 + 83 + 561 = $4,704.60

Pg. 258 9 - 18

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