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1.1. What is 15% of 60?What is 15% of 60?

2.2. 18 is 24% percent of what 18 is 24% percent of what number?number?

3.3. 96 is what percent of 320?96 is what percent of 320?

Consumer MathematicsConsumer MathematicsChapter 11Chapter 11Percent of ChangePercent of Change

Simple InterestSimple InterestCompound InterestCompound InterestConsumer LoansConsumer Loans

Lesson 11.1: PercentLesson 11.1: Percent

The school district receives funds The school district receives funds from several sources. The 2008 from several sources. The 2008 – 2009 budget is $442,300,000. – 2009 budget is $442,300,000. The federal government The federal government contributes $33,500,000 of that contributes $33,500,000 of that amount. What percent does the amount. What percent does the federal government contribute to federal government contribute to the school district’s budget?the school district’s budget?

Percent of ChangePercent of Change

A+ University has decided to A+ University has decided to raise tuition from $7,965 to raise tuition from $7,965 to $8,435 for next year. What is $8,435 for next year. What is the percent of increase in the the percent of increase in the tuition?tuition?

new amount base amountpercent of change =

base amount

Honest Abe’s AutoHonest Abe’s Auto

Abe’s auto is having a blow-out sell. Abe’s auto is having a blow-out sell. Abe advertises that all cars are Abe advertises that all cars are sold at sold at 5% markup5% markup over the over the dealer’s cost. Abe has a new pinto dealer’s cost. Abe has a new pinto for sale for for sale for $18,970$18,970. On the . On the internet you find out that the dealer internet you find out that the dealer cost on this model is cost on this model is $17,500$17,500. Is . Is Abe being honest in his Abe being honest in his advertising? advertising?

Music salesMusic sales

Jamin’ Jude Records reported Jamin’ Jude Records reported that music downloads increased that music downloads increased 28.24% from 2005 to 2006. If 28.24% from 2005 to 2006. If the number of downloads for the number of downloads for 2006 were 524,785 how many 2006 were 524,785 how many downloads were there in 2005?downloads were there in 2005?

Lesson 11.2: InterestLesson 11.2: Interest

Simple Interest:Simple Interest:I = PrtI = PrtI – interest earned, P – principal, I – interest earned, P – principal, r – interest rate, t – time (years)r – interest rate, t – time (years)

Future value:Future value:A = P(1 + rt)A = P(1 + rt)A – future value, P – principal, A – future value, P – principal, r – annual interest rate, t – time in yearsr – annual interest rate, t – time in years

Solve.Solve.

1.1. If you deposit $200 in a savings If you deposit $200 in a savings account paying 6% annual account paying 6% annual interest, how much interest will interest, how much interest will be earned if you leave it there be earned if you leave it there for 5 years?for 5 years?

2.2. If you deposit $500 paying 4.5% If you deposit $500 paying 4.5% annual interest, how much annual interest, how much money will you have in 3 years?money will you have in 3 years?

Solve.Solve.

3.3. Assume that you plan to save Assume that you plan to save $1000 over 2 years to put down on $1000 over 2 years to put down on a car. Your bank offers a certificate a car. Your bank offers a certificate of deposit (CD) that pays 3% annual of deposit (CD) that pays 3% annual interest computed using simple interest computed using simple interest. How much must you put interest. How much must you put in this CD now in order to have the in this CD now in order to have the desired $1000 in 2 years?desired $1000 in 2 years?

Warm-UpWarm-Up1.1. Due to a slump in the economy, Due to a slump in the economy,

Anna’s mutual fund has Anna’s mutual fund has dropped by dropped by 12%12% from last quarter to this quarter. from last quarter to this quarter. If her fund is now worth If her fund is now worth $11,264$11,264, , how much was her fund worth last how much was her fund worth last quarter?quarter?

2.2. How much must you deposit in an How much must you deposit in an account paying account paying 8%8% annual interest annual interest computed using the simple interest computed using the simple interest formula if you earn formula if you earn $800 in 2 years$800 in 2 years??

3.3. You plan to take a trip to the You plan to take a trip to the Grand Canyon in Grand Canyon in 2 years2 years. You . You wish to buy a certificate of wish to buy a certificate of deposit for deposit for $1,200$1,200 that you will that you will cash in for your trip. What cash in for your trip. What annual interest rate must you annual interest rate must you obtain on the certificate if you obtain on the certificate if you need need $1,500$1,500 for your trip? for your trip?

Compound InterestCompound Interest Let’s say you get $250 for your Let’s say you get $250 for your

birthday and you decide to deposit birthday and you decide to deposit the money in a savings account that the money in a savings account that earns 6% interest compounded earns 6% interest compounded annually. How much money would annually. How much money would you have in 3 years?you have in 3 years?

End of year 1: 250(1 + .06(1)) = $265End of year 1: 250(1 + .06(1)) = $265End of year 2: 265(1.06) = $280.90End of year 2: 265(1.06) = $280.90End of year 3: 280.90(1.06) = $297.75End of year 3: 280.90(1.06) = $297.75

What if you left the money in for 15 What if you left the money in for 15 years?years?

A = 250(1.06)A = 250(1.06)1515 = $599.14 = $599.14

So what if the bank compounded the So what if the bank compounded the interest quarterly instead of annually?interest quarterly instead of annually?

: (1 )tShort cut A P r

Compound Interest FormulaCompound Interest Formula

n – n time periods n – n time periods per yearper year1

ntr

A Pn

Compounded quarterly for 3 years: 4 3

.06250 1 $298.90

4A

Compounded quarterly for 15 years: 4 15

.06250 1 $610.80

4A

Selecting the best choice:Selecting the best choice: Your rich Auntie Clause has passed Your rich Auntie Clause has passed

away and bequeathed you away and bequeathed you $20,000$20,000. . Because you are cautious with your Because you are cautious with your investments, you decide to buy a investments, you decide to buy a 5-yr5-yr CD to save for the future. Prudent CD to save for the future. Prudent Savings & Loan has a CD with a yearly Savings & Loan has a CD with a yearly interest rate of interest rate of 5%5% compounded compounded quarterlyquarterly, whereas First Friendly , whereas First Friendly National Bank has a CD with a rate of National Bank has a CD with a rate of 4.8%4.8% compounded compounded monthlymonthly. Which . Which institution gives you the best return institution gives you the best return on your money?on your money?

Saving for collegeSaving for college Jack and Jill just gave birth to Jackill, Jack and Jill just gave birth to Jackill,

their son. They decide to make a their son. They decide to make a deposit into a taxfree account to use deposit into a taxfree account to use later for Jackill’s college education. later for Jackill’s college education. The account has an annual interest The account has an annual interest rate of rate of 8% compounded8% compounded quarterlyquarterly. . How much must they invest now so How much must they invest now so that Jackill will have that Jackill will have $50,000$50,000 at age at age eighteeneighteen??

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1.1. Cameron finds herself in a bind and is Cameron finds herself in a bind and is willing to make a deal. She found the willing to make a deal. She found the perfect prom dress but it costs perfect prom dress but it costs $550!!! Mr. Ike is willing to loan her $550!!! Mr. Ike is willing to loan her the money with the condition that she the money with the condition that she pay it back in 6 months at payments pay it back in 6 months at payments of $100. What interest rate would Mr. of $100. What interest rate would Mr. Ike be earning on his money?Ike be earning on his money?

18.2%

2.2. Decide which is the better Decide which is the better investment:investment:

a)a) 7% compounded yearly or7% compounded yearly or

b)b) 6.8% compounded monthly6.8% compounded monthly

BB

If you invested $500 earning 4.5% If you invested $500 earning 4.5% interest compounded quarterly, interest compounded quarterly, how much money would you have how much money would you have after 20 years?after 20 years?

$1,223.64$1,223.64

Using the log function to solve for Using the log function to solve for ntnt Exponent Property of the Log Function:Exponent Property of the Log Function:

log logxy x yWilliam wants to buy his partners’ half of their game business, Pawnisher’s. Laney and Erica have agreed to sell for $3,000. William presently has $2,700 and found an investment that will pay him 9% annual interest compounded monthly. In how many months will William be able to buy his partners out?

.093000 2700 1

12

nt

101.0075

9nt

10log log(1.0075)

9nt

10log

9log(1.0075)

nt

14.1 ntWilliam will have the money he needs at the end of the 15th month.

10log log(1.0075)

9nt

Finding the interest rateFinding the interest rate

A foundation wants to create a A foundation wants to create a scholarship for a deserving student in scholarship for a deserving student in which the scholarship amount of which the scholarship amount of $500 would come from the interest $500 would come from the interest earned on a scholarshipearned on a scholarship fundfund. The . The foundation has foundation has $1,200$1,200 in the fund in the fund and want to find an annual interest and want to find an annual interest rate that is rate that is compounded monthlycompounded monthly. . What rate of interestWhat rate of interest would they would they need in order to have the $500 for need in order to have the $500 for the scholarship in the scholarship in 4 years?4 years?

12 4

1700 1200 112

r

4817

112 12

r

114848

4817

112 12

r

1.007282781 112

r

0.0874 r

The foundation will need to get an 8.74% interest rate.

p.633 #’s 1-3, 7, 11, 15-16, 20, p.633 #’s 1-3, 7, 11, 15-16, 20, 30,30,

40, 43, 51, 79 40, 43, 51, 79

11.3 Consumer Loans11.3 Consumer Loans Closed-ended credit/ installment loansClosed-ended credit/ installment loans

– loans having a fixed number of equal – loans having a fixed number of equal payments. (furniture, appliances)payments. (furniture, appliances)

Open-ended creditOpen-ended credit – loans where even – loans where even though you are making payments you though you are making payments you may also be increasing the loan by may also be increasing the loan by making further purchases. No set making further purchases. No set number of payments. (Department number of payments. (Department Store charge accounts, Credit cards)Store charge accounts, Credit cards)

Installment LoanInstallment Loan

Often called the Often called the add-on interest add-on interest methodmethod

(1 )monthly payment or

P I P rt

n n

1. Ben buys $2800 worth of furniture. He pays $400 down and agrees to pay the balance at 6% add-on interest for 2 years. Finda) the total amount to be repaid and b) the monthly payment.

Amount to be repaid = P(1 + rt) = $2400(1 + (.06)2)

= $2688

Solution

24 paymentsb) Monthly payment = $2688/24

= $112

Even though the simple interest is Even though the simple interest is easy to compute with the easy to compute with the add-on add-on interest methodinterest method, the actual interest , the actual interest you are paying on the outstanding you are paying on the outstanding balance is higher than the stated balance is higher than the stated interest rate. interest rate. Think about it.Think about it.

Warm-Up/ClassworkWarm-Up/Classwork

p.635 #’s 55, 56, 59, 60, 63p.635 #’s 55, 56, 59, 60, 63 p.643 # 9p.643 # 9

Credit cards & Open-ended creditCredit cards & Open-ended credit The The unpaid balance methodunpaid balance method

computes finance charges (interest) on computes finance charges (interest) on the balance at the end of the previous the balance at the end of the previous month.month.

This method also uses the simple This method also uses the simple interest formula I=Prt, however,interest formula I=Prt, however,

P=previous month’s balance + P=previous month’s balance + finance charge + purchases made – finance charge + purchases made – returns – paymentsreturns – payments

R is the annual interest rate and t = 1/12R is the annual interest rate and t = 1/12

Example: Unpaid Balance MethodExample: Unpaid Balance Method

The table shows a VISA account activity for a 2-month period. If the bank charges an apr of 18% annually with the interest calculated on the unpaid balance each month, find the missing quantities in the table.

MonthMonth Unpaid Unpaid BalancBalance at e at StartStart

FinancFinance e ChargeCharge

PurchasePurchasess

PaymePayment nt

Unpaid Unpaid Balance Balance at Endat End

11 $432.5$432.566

$325.22$325.22 $200$200

22 $877.50$877.50 $1000$1000

Solution

MonthMonth Unpaid Unpaid Balance Balance at Startat Start

FinancFinance e ChargeCharge

PurchasePurchasess

PaymePayment nt

Unpaid Unpaid Balance Balance at Endat End

11 $432.56$432.56 $6.49$6.49 $325.22$325.22 $200$200 $564.2$564.277

22 $564.2$564.277

$8.46$8.46 $877.50$877.50 $1000$1000 $450.2$450.233

Unpaid balance times (.18)(1/12) or .015

Your TurnYour Turn

p.644 # 17p.644 # 17

Finance Charge/Unpaid Balance Finance Charge/Unpaid Balance MethodMethod

Most open-end lenders use a method of calculating finance charges called the average daily balance method. It considers balances on all days of the billing period and comes closer to charging card holders for credit they actually utilize.

The Average Daily Balance MethodThe Average Daily Balance Method1.1. Add the outstanding balance for Add the outstanding balance for

your account for each day of the your account for each day of the previous month.previous month.

2.2. Divide the total in step 1 by the Divide the total in step 1 by the number of days in the previous number of days in the previous month to find the average daily month to find the average daily balance.balance.

3.3. To find the finance charge, use I = To find the finance charge, use I = Prt, where P is the avg. daily Prt, where P is the avg. daily balance, r is the annual interest balance, r is the annual interest rate, and t is the number of days in rate, and t is the number of days in the previous month divided by 365.the previous month divided by 365.

Example: Average Daily BalanceExample: Average Daily Balance

The activity on a credit card account for one billing period is given on the next slide. If the previous balance was $320.75, and the bank charges 16.8% annually, find the average daily balance for the next billing (April 3) and the finance charge for the April 3 billing using the average daily balance method.

Example: Average Daily BalanceExample: Average Daily Balance

March 3 Billing date March 12 Payment $250.00 March 17 Car repairs $422.85 March 20 Food $124.80 April 1 Clothes $64.32

Solution

First we make a table of the running balance

Date Date Running BalanceRunning Balance

March 3March 3 $320.75$320.75

March 12March 12 $320.75 – $250.00 = $70.75$320.75 – $250.00 = $70.75

March 17March 17 $70.75 + $422.85 = $493.60$70.75 + $422.85 = $493.60

March 20March 20 $493.60 + $124.80 = $618.40$493.60 + $124.80 = $618.40

April 1April 1 $618.40 + $64.32 = $682.72$618.40 + $64.32 = $682.72

Take the number of days of the balance times the balance.

Date Date BalanceBalance DaysDays ProductProduct

March 3March 3 $320.75$320.75 99 $2886.75$2886.75

March 12March 12 $70.75$70.75 55 $353.75$353.75

March 17March 17 $493.60$493.60 33 $1480.80$1480.80

March 20March 20 $618.40$618.40 1212 $7420.80$7420.80

April 1April 1 $682.72$682.72 22 $1365.44$1365.44

Find the sum of the daily balances by adding the last column = $13507.54.

Sum of daily balancesAverage daily balance =

Days in billing period

$13507.54

31 $435.73.

Finance charge = ($435.73)(.168)(31/365) = $6.22.

Your TurnYour Turn

p.644 # 23p.644 # 23

Lesson 11.3Lesson 11.3

p.643p.643 #’s 3, 6, 10, 13, 14, 20, 21, #’s 3, 6, 10, 13, 14, 20, 21, 25 25