Math 6 Honors ( Periods 1, 2, & 3)

Simple Interest 9-7
When you borrow money you pay the lender INTEREST for the use of the money. The amount of interest you pay is usually a percent of the amount borrowed figured on a yearly basis. This percent is called the annual rate.

When interest is computed year by year we call it
SIMPLE INTEREST
The formula is I= Prt

Let I = simple interest charges
P = principal ( amount borrowed)
r= annual rate
t = time in years

I = Prt

simple interest is calculated just on the principal.
Let's work through a few examples

How much simple interest would you owe if you borrowed $640 for 3 years at atan annual rate of 15%?

I = Prt
I = (640)(.15)(3)
I = (1920)(.15)
I = 288
$288 in interest

Sarah borrowed $3650 for 4 years at 16% How much must she repay.
Remember she will oe the amount she borrowed as well as the the interest.
I = Prt
I = (3650)(.16)(4)

I =14600(.16)
I = 2336.
Principal + Interest = 3650 + 2336
Sarah owes $5986.


$150 borrowed at 12% annual rate for 1 year

I = Prt

I = (150)(.12)(1)
I = 18
so you would owe $18 in interest after 1 year.
The total due would be $150 + 18 = $168

What if instead you borrowed the same amount but for 2 years... nothing was due until the end of two years
I = Prt
I = 150(.12)(2) = 36
You would owe $36 in interest .. so the total due was 150 + 36 = $ 186.

What if you borrowed the same amount for 3 years...
I = 150(.12)(3) = 54 or $54 in interest.
You would owe 150 + 54 = $ 204 after three years...

However, let's say you could only borrow that amount for 6 months...
I = Prt
I = (150)(.12)(.5)
Why 0.5? that is 1/2 a year.
Now you can always multiply by 1/2 as well.. in fact, sometimes that is easier
I = 150(.12)(1/2) = 9 or $ 9.00

After 6 months you would owe $159.


Dylan paid $375 in interest on a loan of $1500 principal at 12.5% interest.
What was the length of time?

Look at what it is asking and see which of the variables you have...
I= Prt
We have the interest paid, the principal and the annual rate so
375= (1500)(.125)(t)

375 = 187.5t
solve this one step equation by dividing both sides by 187.5

375 = 187.5t
187.5 187.5

t = 2

so 2 years

divide carefully...

Alexis paid $ 585 simple interest on a $6500 loan for 6 months.

what was the annual rate?

What do we know?
I = 585
P = 6500
t= 6 months ( which is 0.5 or 1/2)

I = Prt
585 = 6500 (r)(.5)
585 = 3250r
divide both sides by 3250

585 = 3250r
3250 3250

r = 0.18
which means 18%



annual--> once a year
6 months --> 1/2 or 0.5
4 months--> 1/3
3 months --> 1/4 or 0.25
8 month --> 2/3

(We did not get to this yet... but I thought I would post it... read this..it is interesting to see the difference. We will go over this after STAR testing)
Compound Interest 9-8

Compound interest is ALWAYS more than simple interest.

interest is compounded on the interest!!

$100 savings earning $10 interest/ annual.. [this only happens NOW if your dad is the one paying you... :)]

I = Prt
at the end of the first year
I = 100(.10)(1) = 10 or $10
add that to the 100
$110.
Now for the 2nd year,
$110 is your principal
so
I = Prt
I = 110(.10)(1) = 11 or $11
so at the end of 2 years you have $110 + 11 or $121

Now for the 3rd year
I = Prt
I = 121(10)(1) = $12.10
So at the end of three years you have $121 + 12.10 = $133.10

What if you had $500 at 8% compounded quarterly for one year.

quarterly means 1/4 or .25

I = Prt
I = 500(.08) (1/4)
calculate the 08(1/4) because that will be the constant you will multiply your principal by each time
(.08)(1/4) = .02
so I = 500(.02) = 10
after the first quarter it is 510
I = Prt for the 2nd quarter
I = 510 (.02) = 10.20
so after the 2nd quarter $510 + 10.20 = $520.20
I = Prt for the third quarter
I = 520.20 (0.02) = about $10.40 ( round to the nearest penny)
so after the third quarter
$520.20 + 10.40 = $530.60
I = Prt
I = 530.60(.02) = about $10.61
So at the end of 4 quarters -- or one year
530.60 + 10.61 = $541.21

compounding terms:
annually--> once a year
semiannually --> twice a year
quarterly--> four times a year
monthly--> 12 times a year
daily--> 365 times a year

Math 6 Honors ( Periods 1, 2, & 3)

Commission and Profit 9-6

Some sales jobs pay an amount based on how much you sell. This amount is called a commission.

Like a discount, the commission can be expressed as a percent or as an amount of money.

amount of commission = percent of commission X total sales.

Using the examples from our textbook,

Maria sold $42,000 word of insurance in January. If her commission is 3% of the total sales, what was the amount of her commission in January?

amount of commission = percent X total sales
0.03 X 42,000 = 1260
Her commission was $1,260.

Profit is the difference between total income and total operating costs.

profit = total income – total costs

The percent of profit is the percent of total income that is profit

percent of profit = profit/total income
A shoe store had an income of $8600 and operating costs of $7310. What percent of the store's income was profit?

profit= income- total costs = 8600 -7310 = 1290

percent of profit = profit/total income = 1290/8600 = 0.15
So the percent of profit was 15%.

Practice finding 10%-- its easy--- just move the decimal over one place.
We practiced finding 20%. Just double what you got for 10%.



MATH AT WORK:
Caterer
A caterer provides food for parties, weddings, bar/bat mitzvahs, and other events. Caterers plan the menu, buy the ingredients, and cook the food. Often they provide seating and music as well. For each event, a caterer determines the cost per guest. The catering business requires a thorough knowledge of ratios, proportions, and percents.

Math 6 Honors ( Periods 1, 2, & 3)

Discount and Markup 9-5

A discount is a decrease in the price of an item. A markup is an increase in the price of an item. Both of these changes can be expressed as an amount of money or as a percent of the original price of the item. A store may announce a discount of $3 off the original price of $30 basketball, or a discount of 10%

A warm-up suit that sold for $42.50 is on sale at a 12% discount. What is the sale price?

Method 1: Use the formula

amount of change = percent of change X original amount
= 12% X $42.50

therefore the discount is 0.12 X 42.50 or 5.10
The amount of discount is $5.10
The sale price is 42.50 – 5.10 = $37.40

Method 2: Since the discount is 12%, the sale price is 100% - 12% = 88%.
The sale price is 0.88 X 42.50 = $ 37.40

When you know the amount of discount you subtract to find the new price. When dealing with a markup you add to find the new price.

The price of a new car model was marked up 6% over the previous year’s model. If the previous year’s model sold for $7800, what is the cost of the new car? {and what kind of a car could that be?}
Method 1: Use the formula
amount of change = percent of change X original amount

= 6% X 7800

Therefore the markup is 0.06 X7800= $468
The new price is 7800 + 468 = $8268

Method 2: Since the markup is 6% the new price is 100% + 6% or 106% of the original price. so the new price is 1.06 X7800 = $8268

This year a pair of ice skates sells for $46 after a 15% mark up over last year’s price. What was last year’s price?

This year’s price is 100 + 15 or 115% of last year’s price. Let n present last year’s price
46 = (115/100)n

46 = 1.15n
46/.15 = 1.15n/1.115
40 = n

So last year’s price was $40.

A department store advertised eclectic shavers at a sale price of $36.
If this is a 20% discount, what was the original price?
The sale price is 100 - 20 or 80% of the original price. Let n represent the original price.
36 = (80/100)n
36 = .8n
36/.8 = .8n/.8

45 = n
The original price was $45.
Check to see that your answers are logical and reasonable.

Try these: A service station (that’s gas station, now—they no longer provide service!!) give cash customers a 5% discount on the price of gasoline. If gasoline regularly sells for $3.00 a gallon, what is the discounted price?


A store marks up the price of a $5 item to $12. What is the percent of markup?

Math 6 Honors ( Periods 1, 2, & 3)

Percent of Increase or Decrease 9-4

Let's say we have an iPod that originally sold for $260. It is on sale for $208. What is the amount of change? "How much did you save?"
Just subtract
260-208 = 52
$52.
What is the percent of change?
The percent of change = amount of change/original
52/260 - x/100
or just divide 52 by 260 = .2
which is 20%
REMEMBER: The denominator in the formula is ALWAYS the ORIGINAL AMOUNT.
Amount of change = percent of change X the original amount.
Find the new number when 75 is decreased by 26%
Amount of change - 26% (75
= .26(75)
=19.5
Now take the difference (the amount of change) and subtract THAT from 75
75- 19.5 = 55.5

Remember the circle with the various parts of this formula?

Difference or amount of change
% of change X original amount

Difficult to show here so if you missed these notes make sure to ask a fellow student to see this!! IT is a great way to remember what to do!!

State the increase or decrease. Tell what the amount of change is and the percent of change.
from:
10 to 12
increase
amount of increase: 2
% of change : 20%

4 to 3
decrease
amount of decrease:
% of change : 25%

2 to 5
increase
amount of increase: 3
% of change : 3/2 = 1.5 = 150%

12 to 6
decrease
amount of decrease: 6
% of change : 50%

6 to 12
increase
amount of increase: 6
% of change : 6/6 = 1 = 100%

Find the new number produced when the given number is increased or decrease by the given percent.

120; 20% decrease
120(.20) = 24 120 -24 = 96

30; 10% decrease
30(.10) = 3 30 -3 = 27

48: 50% increase
48(.50) = 24 48 + 24 = 72

128: decrease by 25%, then increased by 25%
What... why multiply by .25 if you can use a fraction and work smarter?
128(1/4) = 32
128 - 32 = 96
then 96 ( 1/4) = 24
96 + 24 = 120

Did you think it would be the starting number? Why wasnn't it?