Pre Algebra Periods 1, 2, & 4

REVIEW REAL LIFE PERCENTS
DISCOUNT = sales price This is similar to mark up , but this time you will SUBTRACT (not add)
A jacket that was $100 is 35% off. (.35)($100) = $35. Sales price = $100 - $35 = $65

DISCOUNT = % OF DECREASE
EX: original price = $200 and sales price = $50. What is the DISCOUNT %? (% of decrease?)
Decrease or discount = $200 - $50 = $150
$150 decrease/$200 original = 3/4 = 75% Discount %

MARKUP = how much you want to make on selling something Then add the markup to get what you want to sell that item for.
EX: you want to make 75% of what you paid (.75)(your cost)
You paid $100 for an ipod. (.75)($100)=$75 markup. So you want to sell it for $175!

MARKUP = a % of INCREASE

EX: Your cost = $50 and your markup = $100. What is your MARKUP %? (% of increase?)
markup = increase
$100 (increase on cost)/$50 (original) = 2 = 200% markup (selling price = $50 + $100 = $150)

CHAPTER 7-8: SIMPLE INTEREST:
Let's talk about different types of interest: credit cards, car loans, mortgages
None of them charge us simple interest, but you need to understand that first:
I =PRT (mneumonic devices "PRINT" or "PARTY")
I = Interest
P = Principal ($ deposited in savings or $ owed to credit card or bank)
R = % (Change it to a decimal or fraction before multiplying)
T = Time (based on one year so if you have 9 months, put it over 12 months or 9/12 of a year)
'
EXAMPLE: You buy an Ipod for $300 on your parent's VISA at 20% and pay it back in 2 years
I = PRT
I = ($300)(.20)(2) = $120 Interest
$300 Ipod + $120 interest to VISA = $420 total cost

EXAMPLE: You deposit $200 in your savings account at Wells Fargo for 9 months at 2%
I = PRT
I = ($200)(.02)(9/12) = $3 interest
$200 deposit + $3 = $203 in your savings account after 9 months

CHAPTER 7-8: COMPOUND INTEREST:
Same as simple, but you charge (or get) INTEREST ON THE INTEREST
So COMPOUND > SIMPLE always!
EXAMPLE: The Ipod above is still bought over 2 years on VISA, but this time interest is COMPOUNDED (added to the principal) ANNUALLY (each year)
After one year: I = ($300)(.20)(1) = $60
$300 Ipod + $60 interest = $360
Now in year 2, you're charged interest on the $360, not just the original $300!
That's why it's always more than SIMPLE interest!
Year two: ($360)(.20)(1) =$72
$360 owed at end of year one + $72 year two interest = $$432 owed at the end of year two
Notice that under SIMPLE interest, that amount was only $420

Interest can be compounded annually (once a year), semiannually (twice a year), quarterly (4 times a year), monthly (12 times a year) or even daily! (365 times a year!)
Which would give you the most interest on your savings deposit? Obviously compounding daily!
Which would give the VISA company the most? Same thing - compounding daily! (that's what they use!)
There's a formula for compound interest:
Balance owed = (principal)(1 + percent rate/# times it compounds a year)^{number of compoundings}
So if I owe VISA $500 at 6% compounded QUARTERLY (4 times a year) and I want to know how much I will owe after 1 year, I can use this formula:
A = P(1 + r/t)ⁿ
A is the amount I'm looking for
P = $500
r = 6% or .06
t = 4 times a year
n = 4 because I want to know after a year and the interest will compound 4 times
A = 500[1 + .06/4]⁴
A = 500(1.015)⁴
A =(500)(1.06136)
A = $530.68

The other way to do this is an organized table:
500(.06)(.25) = $7.50 interest for 1st quarter + $500 = 507.50
$507.5(.06)(.25) = $7.61 interest for 2nd quarter + 507.50 = $515.11
$515.11(.06)(.25) = $7.73 interest for 3rd quarter + $515.11 = $522.84
$522.84(.06)(.25) = $7.84 interest for 4th quarter + $522.84 = $530.68

BUT YOU WOULDN'T WANT TO USE THE TABLE APPROACH FOR MORE THAN ONE YEAR BECAUSE IT JUST TAKES TOO MUCH TIME!