Chapter 13Chapter 13

Consumer Mathematics:Consumer Mathematics:

Buying and SavingBuying and Saving

Section 13.1Section 13.1

Simple and Compound InterestSimple and Compound Interest• GoalsGoals

• Study simple interestStudy simple interest• Calculate interestCalculate interest• Calculate future valueCalculate future value

• Study compound interestStudy compound interest• Calculate future valueCalculate future value

Simple InterestSimple Interest

• If If PP represents the principal, represents the principal, rr the the annual interest rate expressed as a annual interest rate expressed as a decimal, and decimal, and tt the time in years, then the time in years, then the amount of simple interest is:the amount of simple interest is:

I Prt=

Example 1Example 1

• Find the interest on a loan of $100 at Find the interest on a loan of $100 at 6% simple interest for time periods of:6% simple interest for time periods of:

a)a) 1 year1 year

b)b) 2 years2 years

c)c) 2.5 years2.5 years

Example 1, cont’dExample 1, cont’d

• Solution: We have Solution: We have PP = 100 and = 100 and rr = 0.06. = 0.06.

a)a) For For t t = 1 year, the calculation is:= 1 year, the calculation is:

( )( )( )$100 0.06 1 $6I Prt= = =

Example 1, cont’dExample 1, cont’d

• Solution, cont’d: We have Solution, cont’d: We have PP = 100 and = 100 and rr = 0.06. = 0.06.

b)b) For For t t = 2 years, the calculation is:= 2 years, the calculation is:

c)c) For For t t = 2.5 years, the calculation is:= 2.5 years, the calculation is:

( )( )( )$100 0.06 2 $12I Prt= = =

( )( )( )$100 0.06 2.5 $15I Prt= = =

Future ValueFuture Value

• For a simple interest loan, the For a simple interest loan, the future valuefuture value of of the loan is the principal plus the interest.the loan is the principal plus the interest.

• If If PP represents the principal, represents the principal, I I the interest, the interest, rr the annual interest rate, and the annual interest rate, and tt the time in the time in years, then the future value is:years, then the future value is:

( )1F P I P Prt P rt= + = + = +

Example 2Example 2

• Find the future value of a loan of $400 Find the future value of a loan of $400 at 7% simple interest for 3 years.at 7% simple interest for 3 years.

Example 2, cont’dExample 2, cont’d

• Solution: Use the future value formula Solution: Use the future value formula with with PP = 400, = 400, rr = 0.07, and = 0.07, and tt = 3. = 3.• ( )

( )1

400 1 0.07 3 $484

F P rt= +

= + ⋅ =

Example 3Example 3• In 2004, Regular Canada Savings Bonds In 2004, Regular Canada Savings Bonds

paid 1.25% simple interest on the face paid 1.25% simple interest on the face value of bonds held for 1 year. value of bonds held for 1 year.

• If the bond is cashed early, the investor If the bond is cashed early, the investor receives the face value plus interest for receives the face value plus interest for every full month.every full month.

• Suppose a bond was purchased for $8000 Suppose a bond was purchased for $8000 on November 1, 2004.on November 1, 2004.

Example 3, cont’dExample 3, cont’d

a)a) What was the value of the bond if it What was the value of the bond if it was redeemed on November 1, was redeemed on November 1, 2005?2005?

b)b) What was the value of the bond if it What was the value of the bond if it was redeemed on July 10, 2004?was redeemed on July 10, 2004?

Example 3, cont’dExample 3, cont’d

a)a) Solution: If the bond was redeemed Solution: If the bond was redeemed on November 1, 2005, it had been on November 1, 2005, it had been held for 1 year.held for 1 year.

• The future value of the bond after 1 year The future value of the bond after 1 year is:is:

( )( )1

8000 1 0.0125 1 $8100

F P rt= +

= + ⋅ =

Example 3, cont’dExample 3, cont’d

b)b) Solution: If the bond was redeemed Solution: If the bond was redeemed on July 10, 2004, it had been held for on July 10, 2004, it had been held for 7 full months.7 full months.

• The future value of the bond after 7/12 of The future value of the bond after 7/12 of a year is: a year is:

( )

( )1

78000 1 0.0125 $8058.3312

F P rt= +

= + ⋅ ≈

Ordinary InterestOrdinary Interest

• Ordinary interest simplifies calculations Ordinary interest simplifies calculations by using 2 conventions:by using 2 conventions:• Each month is assumed to have 30 days.Each month is assumed to have 30 days.

• Each year is assumed to have 360 days.Each year is assumed to have 360 days.

Example 5Example 5

• A homeowner owes $190,000 on a A homeowner owes $190,000 on a 4.8% home loan with an interest-only 4.8% home loan with an interest-only option.option.• An interest-only option allows the An interest-only option allows the

borrower to pay only the ordinary interest, borrower to pay only the ordinary interest, not the principal, for the first year.not the principal, for the first year.

• What is the monthly payment for the What is the monthly payment for the first year?first year?

Example 5, cont’dExample 5, cont’d

• Solution: Use the simple interest Solution: Use the simple interest formula.formula.

• The monthly payments are:The monthly payments are:

( )( ) 1190000 0.048

12

$760

I Prt⎛ ⎞

= = ⎜ ⎟⎝ ⎠

=

Compound Interest Compound Interest

• Reinvesting the interest, called Reinvesting the interest, called compoundingcompounding, makes the balance grow , makes the balance grow faster.faster.

• To calculate compound interest, you To calculate compound interest, you need the same information as for need the same information as for simple interest plus you need to know simple interest plus you need to know how often the interest is compounded.how often the interest is compounded.

Example 6Example 6

• Suppose a principal of $1000 is Suppose a principal of $1000 is invested at 6% interest per year and invested at 6% interest per year and the interest is compounded annually.the interest is compounded annually.

• Find the balance in the account after 3 Find the balance in the account after 3 years.years.

Example 6, cont’dExample 6, cont’d

• Solution: We must calculate the Solution: We must calculate the interest at the end of each year and interest at the end of each year and then add that interest to the principal.then add that interest to the principal.

• After 1 year:After 1 year:• The interest is:The interest is:

• The new balance is $1060.00The new balance is $1060.00• We could also have used the future value We could also have used the future value

formula.formula.

( )( )( )1000 0.06 1 $60I = =

Example 6, cont’dExample 6, cont’d

• Solution, cont’d:Solution, cont’d:• After 2 years the new balance is:After 2 years the new balance is:

• After 3 years the new balance is:After 3 years the new balance is:

( )( )1

1060 1 0.06 1 $1123.60

F P rt= +

= + ⋅ =

( )( )

1

1123.6 1 0.06 1 $1191.02

F P rt= +

= + ⋅ ≈

Example 6, cont’dExample 6, cont’d

• Solution, cont’d: The interest earned each Solution, cont’d: The interest earned each year increases because of the increasing year increases because of the increasing principal.principal.

Example 6, cont’dExample 6, cont’d

• Solution, cont’d: The following table shows Solution, cont’d: The following table shows the pattern in the calculations for the pattern in the calculations for subsequent years.subsequent years.

Compound InterestCompound Interest• Shortcut formula rather than calculating for each Shortcut formula rather than calculating for each

year: If year: If • PP represents the principal represents the principal• rr the annual interest rate expressed as a decimal, the annual interest rate expressed as a decimal, • mm the number of equal compounding periods per year the number of equal compounding periods per year• tt the time in years the time in years• then the future value of the account is:then the future value of the account is:

1mt

rF P

m⎛ ⎞= +⎜ ⎟⎝ ⎠

Example 7Example 7

• Find the future value of each account at the Find the future value of each account at the end of 3 years if the initial balance is $2457 end of 3 years if the initial balance is $2457 and the account earns:and the account earns:

a)a) 4.5% simple interest. 4.5% simple interest.

b)b) 4.5% compounded annually.4.5% compounded annually.

c)c) 4.5% compounded every 4 months.4.5% compounded every 4 months.

d)d) 4.5% compounded monthly.4.5% compounded monthly.

e)e) 4.5% compounded daily.4.5% compounded daily.

Example 7, cont’dExample 7, cont’d

• Solution: We have Solution: We have PP = 2457 and = 2457 and tt = 3. = 3.

a)a) We have We have r r = 0.045 with simple interest.= 0.045 with simple interest.•

b)b) We have We have r r = 0.045 compounded = 0.045 compounded annually.annually.

•

( )2457 1 0.045 3 $2788.70F = + ⋅ ≈

( ) ( )( )1 31 2457 1 0.045 1

$2803.85

mtF P r m

⋅= + = +

≈

Example 7, cont’dExample 7, cont’d• Solution, cont’d: We have Solution, cont’d: We have rr = 0.045 = 0.045

c)c) Compounded every 4 months:Compounded every 4 months:•

d)d) Compounded monthly:Compounded monthly:•

e)e) Compounded daily:Compounded daily:•

( )( )12 32457 1 0.045 12 $2811.42F

⋅= + ≈

( )( )3 32457 1 0.045 3 $2809.31F

⋅= + ≈

( )( )365 32457 1 0.045 365 $2812.10F

⋅= + ≈

Example 7, cont’dExample 7, cont’d

• Solution, cont’d: The results are Solution, cont’d: The results are summarized below.summarized below.

Section 13.2Section 13.2

LoansLoans• GoalsGoals

• Study amortized loansStudy amortized loans• Use an amortization tableUse an amortization table• Use the amortization formulaUse the amortization formula

• Study rent-to-ownStudy rent-to-own

13.2 Initial Problem13.2 Initial Problem

• Home mortgage rates have decreased and Home mortgage rates have decreased and Howard plans to refinance his home.Howard plans to refinance his home.

• He will refinance $85,000 at either 5.25% He will refinance $85,000 at either 5.25% for 15 years or 5.875% for 30 years.for 15 years or 5.875% for 30 years.

• In each case, what is his monthly payment In each case, what is his monthly payment and how much interest will he pay?and how much interest will he pay?• The solution will be given at the end of the section.The solution will be given at the end of the section.

Simple Interest LoansSimple Interest Loans

• The interest on a The interest on a simple interest loansimple interest loan is simple interest on the amount is simple interest on the amount currently owed.currently owed.

• The simple interest each month is The simple interest each month is called the called the finance chargefinance charge..• Finance charges are calculated using an Finance charges are calculated using an

average daily balanceaverage daily balance and a and a daily interest daily interest raterate..

Example 1Example 1

Example 1, cont’dExample 1, cont’d

• Assuming the billing period is June 10 Assuming the billing period is June 10 through July 9, determine each of the through July 9, determine each of the following:following:

a)a) The average daily balanceThe average daily balance

b)b) The daily percentage rateThe daily percentage rate

c)c) The finance chargeThe finance charge

d)d) The new balanceThe new balance

Example 1, cont’dExample 1, cont’d

a)a) Solution: The daily balances are shown Solution: The daily balances are shown below.below.

Example 1, cont’dExample 1, cont’d

a)a) Solution, cont’d: The average daily Solution, cont’d: The average daily balance is:balance is:

( ) ( ) ( ) ( ) ( )2 287.84 6 333.44 4 183.44 11 203.44 7 281.94

2 6 4 11 7

7521.50$250.72

30

+ + + +

+ + + +

= ≈

Example 1, cont’dExample 1, cont’d

b)b) Solution: The daily percentage rate is:Solution: The daily percentage rate is:

c)c) Solution: The finance charge is the Solution: The finance charge is the simple interest on the average daily simple interest on the average daily balance at the daily rate: balance at the daily rate:

21%0.057534%

365≈

( )( )( )250.72 0.21 365 30 $4.33I = ≈

Example 1, cont’dExample 1, cont’d

d)d) Solution: The new balance is the sum Solution: The new balance is the sum of the previous balance, any new of the previous balance, any new charges, and the finance charge, charges, and the finance charge, minus any payments:minus any payments:

287.84 + 144.10 + 4.33 – 150.00 = 287.84 + 144.10 + 4.33 – 150.00 = 286.27286.27

• The new balance is $286.27.The new balance is $286.27.

Example 1, cont’dExample 1, cont’d

Amortized LoansAmortized Loans• Amortized loansAmortized loans are simple interest loans are simple interest loans

with equal periodic payments over the with equal periodic payments over the length of the loan.length of the loan.

• The important variables for an amortized The important variables for an amortized loan are:loan are:

• PrincipalPrincipal

• Interest rateInterest rate

• Term (length) of the loanTerm (length) of the loan

• Monthly paymentMonthly payment

Amortized Loans, cont’dAmortized Loans, cont’d

• Each payment includes the interest Each payment includes the interest due since the last payment and an due since the last payment and an amount paid toward the balance.amount paid toward the balance.

• The amount paid each month is The amount paid each month is constant, but the split between principal constant, but the split between principal and interest varies.and interest varies.

• The amount of the last payment may be The amount of the last payment may be slightly more or less than usual.slightly more or less than usual.

Example 2Example 2

• Chart the history of an amortized loan Chart the history of an amortized loan of $1000 for 3 months at 12% interest of $1000 for 3 months at 12% interest with monthly payments of $340.with monthly payments of $340.

Example 2, cont’dExample 2, cont’d

• Solution: Monthly payment #1:Solution: Monthly payment #1:• The interest owed isThe interest owed is

• The payment toward the principal is The payment toward the principal is

$340 - $10 = $330 $340 - $10 = $330

• The new balance is $1000 - $330 = $670.The new balance is $1000 - $330 = $670.

( )( )( )11000 0.12 $1012I = =

Example 2, cont’dExample 2, cont’d• Solution, cont’d: Monthly payment #2:Solution, cont’d: Monthly payment #2:

• The interest owed isThe interest owed is

• The payment toward the principal is The payment toward the principal is

$340 - $6.70 = $333.30 $340 - $6.70 = $333.30

• The new balance is $670 - $333.30 = The new balance is $670 - $333.30 = $336.70$336.70

( )( )( )1670 0.12 $6.7012I = =

Example 2, cont’dExample 2, cont’d• Solution, cont’d: Monthly payment #3:Solution, cont’d: Monthly payment #3:

• The interest owed isThe interest owed is

• The remaining balance plus the interest The remaining balance plus the interest is: is: $336.70 + $3.37 = $340.07. $336.70 + $3.37 = $340.07.

• The third and final payment is $340.07.The third and final payment is $340.07.

( )( )( )1336.70 0.12 $3.3712I = ≈

Example 2, cont’dExample 2, cont’d• Solution, cont’d: The amortization Solution, cont’d: The amortization

schedule for this loan is shown below.schedule for this loan is shown below.

Example 3Example 3• A couple is buying a vehicle for $20,995.A couple is buying a vehicle for $20,995.• They pay $7000 down and finance the They pay $7000 down and finance the

remainder at an annual interest rate of 4.5% remainder at an annual interest rate of 4.5% for 48 months.for 48 months.

• Use the amortization table to determine Use the amortization table to determine their monthly payment. (For any assignment their monthly payment. (For any assignment you may use an amortization calculator on you may use an amortization calculator on the internet)the internet)

Example 3, cont’dExample 3, cont’d

• Solution: The amount being financed is Solution: The amount being financed is $20,995 – $7000 = $13,995.$20,995 – $7000 = $13,995.

• In the table, find the row corresponding In the table, find the row corresponding to 4.5% and the column corresponding to 4.5% and the column corresponding to 4 years.to 4 years.• This entry is highlighted on the next slide.This entry is highlighted on the next slide.

Example 3, cont’dExample 3, cont’d

Example 3, cont’dExample 3, cont’d

• Solution, cont’d: The value 22.803486 Solution, cont’d: The value 22.803486 indicates the couple will pay indicates the couple will pay $22.803486 for each $1000 they $22.803486 for each $1000 they borrowed.borrowed.•

• They will pay $319.14 per month.They will pay $319.14 per month.

( )( )22.803486 13.995 319.13479≈

Rent-to-OwnRent-to-Own

• In a rent-to-own transaction, you rent In a rent-to-own transaction, you rent the item at a monthly rate, but after a the item at a monthly rate, but after a contracted number of payments, the contracted number of payments, the item becomes yours.item becomes yours.

• The difference between the retail price The difference between the retail price of the item and the total of your of the item and the total of your monthly payments is the interest.monthly payments is the interest.

Example 8Example 8

• Suppose you can rent-to-own a $500 Suppose you can rent-to-own a $500 television for 24 monthly payments of $30.television for 24 monthly payments of $30.

a)a) What amount of interest would you pay for What amount of interest would you pay for the rent-to-own television?the rent-to-own television?

b)b) What annual rate of simple interest on What annual rate of simple interest on $500 for 24 months yields the same $500 for 24 months yields the same amount of interest found in part (a)?amount of interest found in part (a)?

Example 8, cont’dExample 8, cont’d

a)a) Solution: Solution: • The total of your monthly payments will The total of your monthly payments will

be 24($30) = $720.be 24($30) = $720.

• You will pay $720 - $500 = $220 in You will pay $720 - $500 = $220 in interest over the 2 years.interest over the 2 years.

Example 8, cont’dExample 8, cont’d

b)b) Solution: Solution: • Solve the simple interest formula for Solve the simple interest formula for rr::

• The equivalent simple interest rate is:The equivalent simple interest rate is:

Ir

Pt=

( )( )220

0.22 22%500 2

r = = =

13.2 Initial Problem Solution13.2 Initial Problem Solution• Home mortgage rates have decreased Home mortgage rates have decreased

and Howard plans to refinance his and Howard plans to refinance his home. He will refinance $85,000 at home. He will refinance $85,000 at either 5.25% for 15 years or 5.875% either 5.25% for 15 years or 5.875% for 30 years.for 30 years.

• In each case, what is his monthly In each case, what is his monthly payment and how much interest will payment and how much interest will he pay?he pay?

Initial Problem Solution, cont’dInitial Problem Solution, cont’d

• The 15-year loan has an interest rate of The 15-year loan has an interest rate of 5.25%.5.25%.

• According to the amortization table, the According to the amortization table, the monthly payment per $1000 would be monthly payment per $1000 would be $8.038777.$8.038777.

• Under this loan, Howard’s monthly Under this loan, Howard’s monthly payment would be $8.038777(85) payment would be $8.038777(85) which is approximately $683.30.which is approximately $683.30.

Initial Problem Solution, cont’dInitial Problem Solution, cont’d

• For the 15-year loan, Howard will pay a For the 15-year loan, Howard will pay a total of ($683.30)(12)(15) = $122,994.total of ($683.30)(12)(15) = $122,994.

• The amount spent on interest is The amount spent on interest is $122,994 - $85,000 = $37,994.$122,994 - $85,000 = $37,994.

Initial Problem Solution, cont’dInitial Problem Solution, cont’d

• The 30-year loan has an interest rate of The 30-year loan has an interest rate of 5.875%, which is not found in the table.5.875%, which is not found in the table.

• Using the amortization formula, we find Using the amortization formula, we find a monthly payment amount of $502.81.a monthly payment amount of $502.81.

Initial Problem Solution, cont’dInitial Problem Solution, cont’d

• For the 30-year loan, Howard will pay a For the 30-year loan, Howard will pay a total of ($502.81)(12)(30) = total of ($502.81)(12)(30) = $181,011.60.$181,011.60.

• The amount spent on interest is The amount spent on interest is $181,011.60 - $85,000 = $96,011.60$181,011.60 - $85,000 = $96,011.60

Section 13.3Section 13.3

Buying a HouseBuying a House

• GoalsGoals

• Study affordability guidelinesStudy affordability guidelines

• Study mortgagesStudy mortgages• Interest rates and closing costsInterest rates and closing costs• Annual percentage ratesAnnual percentage rates• Down paymentsDown payments

13.3 Initial Problem13.3 Initial Problem

• Suppose you have saved $15,000 toward a down Suppose you have saved $15,000 toward a down payment on a house and your total yearly income is payment on a house and your total yearly income is $45,000. What is the most you could afford to pay $45,000. What is the most you could afford to pay for a house?for a house?

• Assume you pay 0.5% of the value for insurance, Assume you pay 0.5% of the value for insurance, you pay 1.5% of the value for taxes, your closing you pay 1.5% of the value for taxes, your closing costs will be $2000, and you can obtain a fixed-rate costs will be $2000, and you can obtain a fixed-rate mortgage for 30 years at 6% interest. mortgage for 30 years at 6% interest. • The solution will be given at the end of the section.The solution will be given at the end of the section.

Affordability GuidelinesAffordability Guidelines

• The 2 most common guidelines for buying a The 2 most common guidelines for buying a house are:house are:• The maximum house price is 3 times your annual The maximum house price is 3 times your annual

gross income.gross income.

• Your maximum monthly housing expenses Your maximum monthly housing expenses should be 25% of your gross monthly income. should be 25% of your gross monthly income. (housing expenses include mortgage payment, (housing expenses include mortgage payment, insurance and property taxes)insurance and property taxes)

Example 1Example 1

• If your annual gross income is $60,000, If your annual gross income is $60,000, what do the guidelines tell you about what do the guidelines tell you about purchase price and monthly expenses purchase price and monthly expenses for your potential home purchase?for your potential home purchase?

Example 1, cont’dExample 1, cont’d

• Solution: Solution: • The purchase price should be no more The purchase price should be no more

than 3($60,000) = $180,000.than 3($60,000) = $180,000.

• The The monthlymonthly (multiply by 1/12) expenses (multiply by 1/12) expenses for mortgage payments, property taxes, for mortgage payments, property taxes, and homeowner’s insurance should be no and homeowner’s insurance should be no more than more than ( )( )0.25 1 12 60000 $1250.=

Affordability Guidelines, cont’dAffordability Guidelines, cont’d

• Some lenders allow monthly expenses Some lenders allow monthly expenses up to 38% of the buyer’s monthly up to 38% of the buyer’s monthly income.income.• We call the 25% level the low maximum We call the 25% level the low maximum

monthly housing expense estimate.monthly housing expense estimate.

• We call the 38% level the high maximum We call the 38% level the high maximum monthly housing expense estimate.monthly housing expense estimate.

Example 2Example 2

• Suppose Andrew and Barbara both Suppose Andrew and Barbara both have jobs, each earning $24,000 a year, have jobs, each earning $24,000 a year, and they have no debts.and they have no debts.

• What are the low and high estimates of What are the low and high estimates of how much they can afford to pay for how much they can afford to pay for monthly housing expenses?monthly housing expenses?

Example 2, cont’dExample 2, cont’d

• Solution: The low estimate is 25% of the Solution: The low estimate is 25% of the total monthly income.total monthly income.•

• The high estimate is 38% of the total The high estimate is 38% of the total monthly income.monthly income.•

48,0000.25 $1000

12⎛ ⎞=⎜ ⎟⎝ ⎠

48,0000.38 $1520

12⎛ ⎞=⎜ ⎟⎝ ⎠

MortgagesMortgages

• A A mortgagemortgage is a loan that is guaranteed is a loan that is guaranteed by real estate.by real estate.

• The interest rate of a The interest rate of a fixed-rate fixed-rate mortgagemortgage is set for the entire term. is set for the entire term.

• The interest rate of an The interest rate of an adjustable-rate adjustable-rate mortgage (ARM)mortgage (ARM) can change. can change.

Mortgages, cont’dMortgages, cont’d

• The finalizing of a house purchase is called The finalizing of a house purchase is called the the closingclosing..

• PointsPoints are fees paid to the lender at the time are fees paid to the lender at the time of the closing.of the closing.• Loan origination feesLoan origination fees

• Discount chargesDiscount charges

• Points and any other expenses paid at the Points and any other expenses paid at the time of the closing are called time of the closing are called closing costsclosing costs..

Example 3Example 3• Suppose you will borrow $80,000 for a home at 6.5% Suppose you will borrow $80,000 for a home at 6.5%

interest on a 30-year fixed-rate mortgage.interest on a 30-year fixed-rate mortgage.• The loan involves a one-point loan origination fee and a The loan involves a one-point loan origination fee and a

one-point discount charge. What are your added costs?one-point discount charge. What are your added costs?

• Note: One point is equal to 1 percent of the loan amount.Note: One point is equal to 1 percent of the loan amount.

• Solution: Each fee will cost you 1% of $80,000, or $800.Solution: Each fee will cost you 1% of $80,000, or $800.• Your total added fees are $1600.Your total added fees are $1600.

Down PaymentDown Payment• A A down paymentdown payment on a house is the amount of on a house is the amount of

cash the buyer pays at closing, minus any cash the buyer pays at closing, minus any points and fees.points and fees.

• Traditionally a down payment is 20% of the Traditionally a down payment is 20% of the value, but can be lower. value, but can be lower.

• If you have $25,000 for a down payment, If you have $25,000 for a down payment, what is the highest-priced home you can what is the highest-priced home you can afford if a 20% down payment is required?afford if a 20% down payment is required?

• Solution: The maximum price you can Solution: The maximum price you can afford to pay is your down payment afford to pay is your down payment amount divided by 20%.amount divided by 20%.

•

• The most expensive house you can afford The most expensive house you can afford is one that is selling for $125,000. is one that is selling for $125,000.

25,000$125,000

0.20=

13.3 Initial Problem Solution13.3 Initial Problem Solution• Suppose you have saved $15,000 toward a Suppose you have saved $15,000 toward a

down payment on a house and your total down payment on a house and your total yearly income is $45,000. What is the most yearly income is $45,000. What is the most you could afford to pay for a house?you could afford to pay for a house?

• Assume you pay 0.5% of the value for Assume you pay 0.5% of the value for insurance, you pay 1.5% of the value for insurance, you pay 1.5% of the value for taxes, your closing costs will be $2000, and taxes, your closing costs will be $2000, and you can obtain a fixed-rate mortgage for 30 you can obtain a fixed-rate mortgage for 30 years at 6% interest.years at 6% interest.

Initial Problem Solution, cont’dInitial Problem Solution, cont’d

• Your total income is $45,000Your total income is $45,000• You have $15,000 saved for the You have $15,000 saved for the

purchasepurchase• $2000 will be used for closing costs.$2000 will be used for closing costs.

• This leaves $13,000 for a down This leaves $13,000 for a down payment.payment.

Initial Problem Solution, cont’dInitial Problem Solution, cont’d

• The first affordability guideline says you can The first affordability guideline says you can spend at most 3($45,000) = $135,000 on a spend at most 3($45,000) = $135,000 on a house.house.

• $135,000 - 13,000 = $122,000 to finance.$135,000 - 13,000 = $122,000 to finance.• Next, consider your monthly expenses:Next, consider your monthly expenses:

• You would be financing $122,000 at 6% for 30 years.You would be financing $122,000 at 6% for 30 years.

• The monthly mortgage payments would be The monthly mortgage payments would be 122($5.995505) = $732. (from the table or website 122($5.995505) = $732. (from the table or website calculator.)calculator.)

Initial Problem Solution, cont’dInitial Problem Solution, cont’d

• The insurance and taxes are 2% of the home’s The insurance and taxes are 2% of the home’s value annually.value annually.• This adds $225 to the monthly expenses, for a total This adds $225 to the monthly expenses, for a total

monthly expense of $732 + $225 = $957.monthly expense of $732 + $225 = $957.

• According to the second affordability guideline According to the second affordability guideline you can only afford monthly expenses of at most you can only afford monthly expenses of at most $938.$938.

• ($45,000/12=$3750 and then .25 of ($45,000/12=$3750 and then .25 of $3750=$938)$3750=$938)• The monthly expenses for this house are above your The monthly expenses for this house are above your

maximum. You cannot afford it.maximum. You cannot afford it.

Initial Problem Solution, cont’dInitial Problem Solution, cont’d

• A house priced $135,000 is slightly A house priced $135,000 is slightly out of your reach, so your options are:out of your reach, so your options are:• Wait for interest rates to fall.Wait for interest rates to fall.

• Increase your income.Increase your income.

• Come up with a larger down payment.Come up with a larger down payment.

• Choose a less expensive house.Choose a less expensive house.

Dave Ramsey’s website

http://www.daveramsey.com/

Chapter 13 Assignmentdue Tues August 12

• Section 13.1 pg 812 Show use of a formula on each problem (1, 3, 13a, 27, 28 and find the most recently released CPI - I think it was in the news last week.)

• Section 13.2 pg 829(3, 9, 11, 15, 21 *** for 15 and 21 use an amortization website calculator)

• Section 13.3 pg 842 Show work on each problem (1, 5, 7, 9, 13, 14, 23)

• NOTE: You may use an amortization website to calculate any amortization rather than the textbook table.