Transcript Consumer Mathematics Chapter 11

Warm - Up
1.
2.
3.
What is 15% of 60?
18 is 24% percent of what number?
96 is what percent of 320?
Consumer Mathematics
Chapter 11
Percent of Change
Simple Interest
Compound Interest
Consumer Loans
Lesson 11.1: Percent

The school district receives funds
from several sources. The 2008 –
2009 budget is $442,300,000. The
federal government contributes
$33,500,000 of that amount. What
percent does the federal government
contribute to the school district’s
budget?
Percent of Change
new amount  base amount
percent of change =
base amount

A+ University has decided to raise
tuition from $7,965 to $8,435 for next
year. What is the percent of increase
in the tuition?
Honest Abe’s Auto

Abe’s auto is having a blow-out sell.
Abe advertises that all cars are sold
at 5% markup over the dealer’s cost.
Abe has a new pinto for sale for
$18,970. On the internet you find
out that the dealer cost on this model
is $17,500. Is Abe being honest in
his advertising?
Music sales

Jamin’ Jude Records reported that
music downloads increased 28.24%
from 2005 to 2006. If the number of
downloads for 2006 were 524,785
how many downloads were there in
2005?
Lesson 11.2: Interest

Simple Interest:
I = Prt
I – interest earned, P – principal,
r – interest rate, t – time (years)

Future value:
A = P(1 + rt)
A – future value, P – principal,
r – annual interest rate, t – time in years
Solve.
1.
2.
If you deposit $200 in a savings
account paying 6% annual interest,
how much interest will be earned if
you leave it there for 5 years?
If you deposit $500 paying 4.5%
annual interest, how much money
will you have in 3 years?
Solve.
3.
Assume that you plan to save $1000
over 2 years to put down on a car. Your
bank offers a certificate of deposit (CD)
that pays 3% annual interest computed
using simple interest. How much must
you put in this CD now in order to have
the desired $1000 in 2 years?
Warm-Up
1.
2.
Due to a slump in the economy, Anna’s
mutual fund has dropped by 12% from
last quarter to this quarter. If her fund is
now worth $11,264, how much was her
fund worth last quarter?
How much must you deposit in an
account paying 8% annual interest
computed using the simple interest
formula if you earn $800 in 2 years?
3.
You plan to take a trip to the Grand
Canyon in 2 years. You wish to buy
a certificate of deposit for $1,200
that you will cash in for your trip.
What annual interest rate must you
obtain on the certificate if you need
$1,500 for your trip?
Compound Interest

Let’s say you get $250 for your birthday
and you decide to deposit the money in a
savings account that earns 6% interest
compounded annually. How much money
would you have in 3 years?
End of year 1: 250(1 + .06(1)) = $265
End of year 2: 265(1.06) = $280.90
End of year 3: 280.90(1.06) = $297.75
What if you left the money in for 15
years?
Short  cut : A  P(1  r )
t
A = 250(1.06)15 = $599.14

So what if the bank compounded the
interest quarterly instead of annually?
Compound Interest Formula
 r
A  P 1  
 n
nt
n – n time periods
per year
Compounded quarterly for 3 years:
 .06 
A  250 1 

4 

43
 $298.90
Compounded quarterly for 15 years:
 .06 
A  250 1 

4 

4 15
 $610.80
Selecting the best choice:

Your rich Auntie Clause has passed away
and bequeathed you $20,000. Because
you are cautious with your investments,
you decide to buy a 5-yr CD to save for
the future. Prudent Savings & Loan has a
CD with a yearly interest rate of 5%
compounded quarterly, whereas First
Friendly National Bank has a CD with a
rate of 4.8% compounded monthly.
Which institution gives you the best return
on your money?
Saving for college

Jack and Jill just gave birth to Jackill, their
son. They decide to make a deposit into a
taxfree account to use later for Jackill’s
college education. The account has an
annual interest rate of 8% compounded
quarterly. How much must they invest
now so that Jackill will have $50,000 at
age eighteen?
Warm-Up
1.
Cameron finds herself in a bind and is
willing to make a deal. She found the
perfect prom dress but it costs $550!!!
Mr. Ike is willing to loan her the money
with the condition that she pay it back in
6 months at payments of $100. What
interest rate would Mr. Ike be earning on
his money?
18.2%
2.
Decide which is the better investment:
a)
b)
7% compounded yearly or
6.8% compounded monthly
B

If you invested $500 earning 4.5%
interest compounded quarterly, how
much money would you have after 20
years?
$1,223.64
Using the log function to solve for nt

Exponent Property of the Log Function:
log y  x log y
x
William 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?
nt
 .09 
3000  2700 1 

 12 
 10 
log    nt log(1.0075)
10
nt
9
 1.0075
9
10
 10 
nt
log    log(1.0075)
9
 
log  
 9   nt
log(1.0075)
14.1  nt
William will have the money he needs at the
end of the 15th month.
Finding the interest rate

A foundation wants to create a scholarship
for a deserving student in which the
scholarship amount of $500 would come
from the interest earned on a scholarship
fund. The foundation has $1,200 in the
fund and want to find an annual interest
rate that is compounded monthly. What
rate of interest would they need in order
to have the $500 for the scholarship in 4
years?
12 4
r 

1700  1200 1  
 12 
r 
 17  
   1  
 12   12 
 17 
 
 12 
1
48
48
48

r  
  1   
  12  


r
1.007282781  1 
12
0.0874  r
1
48
The foundation will
need to get an 8.74%
interest rate.

p.633 #’s 1-3, 7, 11, 15-16, 20, 30,
40, 43, 51, 79
11.3 Consumer Loans

Closed-ended credit/ installment loans –
loans having a fixed number of equal
payments. (furniture, appliances)

Open-ended credit – loans where even
though you are making payments you may
also be increasing the loan by making
further purchases. No set number of
payments. (Department Store charge
accounts, Credit cards)
Installment Loan

Often called the add-on interest
method
PI
P(1  rt )
monthly payment 
or
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. Find
a) the total amount to be repaid and
b) the monthly payment.
Solution
Amount to be repaid = P(1 + rt)
= $2400(1 + (.06)2)
= $2688
b) Monthly payment = $2688/24
= $112

24 payments
Even though the simple interest is easy to
compute with the add-on interest method,
the actual interest you are paying on the
outstanding balance is higher than the
stated interest rate. Think about it.
Warm-Up/Classwork


p.635 #’s 55, 56, 59, 60, 63
p.643 # 9
Credit cards & Open-ended credit


The unpaid balance method computes
finance charges (interest) on the balance
at the end of the previous month.
This method also uses the simple interest
formula I=Prt, however,
P=previous month’s balance +
finance charge + purchases made –
returns – payments
R is the annual interest rate and t = 1/12
Example: Unpaid Balance Method

The table shows a VISA account activity for a 2month 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.
Month
1
2
Unpaid
Balance
at Start
$432.56
Finance
Charge
Purchases
Payment Unpaid
Balance
at End
$325.22
$200
$877.50
$1000
 Solution
Month Unpaid
Balance
at Start
Finance
Charge
Purchases
Payment Unpaid
Balance
at End
1
$432.56
$6.49
$325.22
$200
$564.27
2
$564.27
$8.46
$877.50
$1000
$450.23
Unpaid balance times (.18)(1/12) or .015
Your Turn
 p.644
# 17
Finance Charge/Unpaid Balance
Method

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 Method
1.
2.
3.
Add the outstanding balance for your
account for each day of the previous
month.
Divide the total in step 1 by the number
of days in the previous month to find the
average daily balance.
To find the finance charge, use I = Prt,
where P is the avg. daily balance, r is the
annual interest rate, and t is the number
of days in the previous month divided by
365.
Example: 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 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
Running Balance
March 3
$320.75
March 12
$320.75 – $250.00 = $70.75
March 17
$70.75 + $422.85 = $493.60
March 20
$493.60 + $124.80 = $618.40
April 1
$618.40 + $64.32 = $682.72
Take the number of days of the balance times the
balance.
Date
Balance
Days
Product
March 3
$320.75
9
$2886.75
March 12
$70.75
5
$353.75
March 17
$493.60
3
$1480.80
March 20
$618.40
12
$7420.80
April 1
$682.72
2
$1365.44
Find the sum of the daily balances by
adding the last column = $13507.54.
Sum of daily balances
Average daily balance =
Days in billing period
$13507.54

31
 $435.73.
Finance charge = ($435.73)(.168)(31/365) = $6.22.
Your Turn
 p.644
# 23

Lesson 11.3
p.643 #’s 3, 6, 10, 13, 14, 20, 21, 25