Percents applications.notebook April 07, 2016

Transcription

1 Applications with Percents Working with percents is something that people do all the time. The goal for the next few days is to identify how/where we encounter percents in our every day lives and learn to solve some everyday problems associated with percents. To start... Where might we encounter percents in our lives?

2 a) Sales Tax In Ontario, we have to pay HST (Harmonized Sales Tax) on most items that we purchase. In Ontario, we pay 13% sales tax (8% provincial rate + 5 % federal rate) on most items Some exceptions: books, children's clothing: 5 % prepared food items that cost less than $4.00: 0 % basic groceries: 0 %

3 Ways to calculate sales tax: Let's start with a basic one. You purchase a video game that costs $ (before taxes). How much will your total bill be? $ How can we calculate this?

4 Ways to calculate sales tax: 1. Find 13 percent of the total price (before taxes) then add the tax to the original cost. 13 percent of $100 = 0.13 x $100 = $13.00 $100 (original cost) + $13.00 (tax) = $ Find 113 percent of the total price. 113 percent of $100 = 1.13 x $100 = $ Use your estimation skills to get close. Find 10 percent of the total (move your decimal one place to the left) then find one percent (move decimal 2 places left). Multiply the 1% by 3 (to get 3%) then add that total to the 10 % 10 % of = $10.00, 1% of $ = $1.00; 3($1.00) + $10.00) = $13.00 tax.

5 Ways to calculate sales tax: 1. Find 13 percent of the total price (before taxes) then add the tax to the original cost. 13 percent of $100 = 0.13 x $100 = $13.00 $100 (original cost) + $13.00 (tax) = $ You Practice: Find the total cost of each item after taxes: a) A pair of hockey skates that cost $ Find 113 percent of the total price. 113 percent of $100 = 1.13 x $100 = $ Use your estimation skills to get close. Find 10 percent of the total (move your decimal one place to the left) then find one percent (move decimal 2 places left). Multiply the 1% by 3 (to get 3%) then add that total to the 10 % 10 % of = $10.00, 1% of $ = $1.00; 3 ($1.00) + $10.00) = $13.00 tax. b) A case of Coca Cola that costs $4.49 c) A one month Netflix subscription that costs $8.99

6 Taxes elsewhere. The tax rate isn't 13% everywhere for everyone. tax calculator hst gst.html (sales tax in different provinces) (sales tax in USA) *How much would you save if you purchased the same three products if you lived in Alberta (5% tax rate)? *How much more would the three products cost you if you lived in Quebec (14.975% tax rate)? a) A pair of hockey skates that cost $ b) A case of Coca Cola that costs $4.49 c) A one month Netflix subscription that costs $8.99

7 Challenge: You got a bill for a new television that had a total of $ You live in Ontario. Your parents told you that they would pay for your taxes if you could use your Math skills to show them how much the tax cost. Would you get some money from your parents?

8 Challenge: You got a bill for a new television that had a total of $ You live in Ontario. Your parents told you that they would pay for your taxes if you could use your Math skills to show them how much the tax cost. Would you get some money from your parents?

9 Challenge: You got a bill for a new television that had a total of $ You live in Ontario. Your parents told you that they would pay for your taxes if you could use your Math skills to show them how much the tax cost. Would you get some money from your parents?

10 B. Discounts Sometimes, when you go shopping, you might be lucky enough to find something that you want that is discounted/on sale. *When something is discounted, it means that we pay less than 100% of the original price. For example: If a pair of jeans have a price of $50.00 but they are 20 % off, it would mean that we pay 80 percent of the original price. How much would the jeans cost after the discount was applied? (assume no taxes for this example)

11 If a pair of jeans have a price of $50.00 but they are 20 % off, it would mean that we pay 80 percent of the original price. Strategies: a) Find out what 20 percent of the original cost is then subtract the discount from the original price. 20 percent of $50.00 = 0.20 x $50.00 = $10.00 $50.00 (original price) $10.00 (discount) = $40.00 (discounted price) b) Subtract the discounted percent from 100% to find out what percentage of the original price you need to pay (then calculate that percent) 100 percent 20 percent = 80 of original price 0.80 x $50.00 = $40.00 c) Use mental math/estimation to calculate the discount. move the decimal 1 place to the left to find 10 % of original price ($50.00: 10 % = $5.00) multiply 10% by 2 to get 20% ($5.00 x 2 = $10.00)

12 Strategies: a) Find out what 20 percent of the original cost is then subtract the discount from the original price. 20 percent of $50.00 = 0.20 x $50.00 = $10.00 $50.00 (original price) $10.00 (discount) = $40.00 (discounted price) Now you try: A book costs $29.99 originally but it is being sold for 40% off. What will the book cost (before taxes)? b) Subtract the discounted percent from 100% to find out what percentage of the original price you need to pay (then calculate that percent) 100 percent 20 percent = 80 of original price 0.80 x $50.00 = $40.00 c) Use mental math/estimation to calculate the discount. move the decimal 1 place to the left to find 10 % of original price ($50.00: 10 % = $5.00) multiply 10% by 2 to get 20% ($5.00 x 2 = $10.00)

13 When there is tax AND a discount Step 1: Calculate the discount Step 2: Calculate the tax from the discounted price Example: You go to a restaurant and buy a breakfast that costs $ You have a 25% off coupon. 1. $12.99 x 0.75 = $ (round to $9.74) 2. $9.74 x 1.13 = $ (round to $11.01) *Now, what if I want to add a tip?:)

14 Challenge: You use a coupon for 10% off to buy a CD that is on sale at a discount of 15%. Do you end up with a discount of 25% on the regular price of the CD? Explain.

15 C. Interest Interest can be a good thing for you or a bad thing for you, depending on your situation Good interest (for you) If you have money in your bank account, you the bank PAYS YOU interest. *Tangerine Bank currently offers 2.40 % annual interest in their Savings Accounts(special promotion) **Update: Mr. Thompson just got an e mail from Tangerine as he was making this. The newest promotion is 3.00% Bad interest (for you) If you owe money on your credit card, YOU PAY the credit card interest *PC MasterCard's current annual interest rate is 19.97% *Why do you think credit card rates (negatives for customers) are so much higher than interest paid on bank balances (positives for customers)?

16 Types of Interest: There are LOTS of different formulas that might be used to calculate interest, but there are two main ones: Simple interest interest that only calculates the principal amount of the loan/investment. Formula: Interest = P x r x t (P= principal; money borrowed/invested, r = annual interest rate as a decimal, t = time in years) Compound Interest interest that is recalculated to include the principal AND the accumulated interest (interest on top of interest) Formula(s): There are different formulas to calculate compound interest that depend on which type of compound interest you are calculating) One example (Not a Grade 8 expectation; don't worry:) number of times interest is compounded

17 Calculating interest Interest paid/owed is usually based on an annual (over the course of a year) rate but it is often paid out/collected on a monthly basis. *How do we calculate monthly interest payments based on annual rates? Principal (amount of money) x annual rate (as a decimal) x 1/12 *why 1/12?

18 Example question: Hannah has $ in her Tangerine account. If the annual interest rate is 2.40%, a) How much total interest will Hannah have after 6 months, if it is simple interest? Simple interest = P x r x t; P = $5000, r = 2.4% = 0.024, t = 6/12 = 1/2 I = $5000 x x 1/2 =$60 Therefore, Hannah would make $60 in interest over 6 months. b) How much will Tangerine pay Hannah in interest at the end of the month (if it is compound interest? 5000 x x 1/12 = $10 Therefore, Hannah would earn $10 in interest the first month c) How much will be in Hannah's bank account after 6 months if she is paid periodic compound interest (paid once each month)? after 1 month: $5010 total (Hannah's money plus interest from part (b) after 2 months: $5010 x x 1/12 = $10.02 interest; $ $10.02 = $ after 3: $ x x 1/12 = $10.04; $ $10.04 = $ after 4: $ x x 1/12 = $10.06; $ $10.06 = $ after 5: $ x x 1/12 = $10.08; $ $10.08 = $ after 6; $ x x 1/12 = $10.10; $ $ $10.10 = $ Therefore, after 6 months, Hannah would have $ in her account if interest was paid using periodic compound interest. **Over 6 months, what percent interest did she make on her investment? **Why does the answer not 2.4%? Or, using the formula: t =number of times interest is compounded A = 5000 ( /12) 12x 0.5 =5000(1.002) 6 =5000( ) =$ ***After 6 months, there would only be a difference of $0.30 (or 30 cents) if we looked at periodic compound vs. simple interest. Why does it matter; its only 30 cents?!?! (We all know Dalton wants to ask this question)

19 Example question: Hannah has $ in her Tangerine account. If the annual interest rate is 2.40%, a) How much total interest will Hannah have after 6 months, if it is simple interest? Simple interest = P x r x t; P = $5000, r = 2.4% = 0.024, t = 6/12 = 1/2 I = $5000 x x 1/2 =$60 Therefore, Hannah would make $60 in interest over 6 months. b) How much will Tangerine pay Hannah in interest at the end of the month (if it is compound interest? 5000 x x 1/12 = $10 Therefore, Hannah would earn $10 in interest the first month c) How much will be in Hannah's bank account after 6 months if she is paid periodic compound interest (paid once each month)? after 1 month: $5010 total (Hannah's money plus interest from part (b) after 2 months: $5010 x x 1/12 = $10.02 interest; $ $10.02 = $ after 3: $ x x 1/12 = $10.04; $ $10.04 = $ after 4: $ x x 1/12 = $10.06; $ $10.06 = $ after 5: $ x x 1/12 = $10.08; $ $10.08 = $ after 6; $ x x 1/12 = $10.10; $ $ $10.10 = $ Therefore, after 6 months, Hannah would have $ in her account if interest was paid using periodic compound interest. A = 5000 ( /1212 x 6/12 =5000(1.002) 6 =5000( ) =$ number of times interest is compounded Now you Try... Mr. Thompson's PC MasterCard has a balance of $ on it. The annual interest rate is 19.97% a) how much interest will Mr. Thompson be charged at the end of the month? b) If the bank charged simple interest for the course of one year, but Mr. Thompson wanted to pay off this bill in monthly installments, how much would he pay each month? c) Bonus: If the bank used periodic compound interest (calculated at the end of every month), and Mr. Thompson didn't make any payments until the end of the year, how much would he owe MasterCard?

20 Challenge: Dalton needs to borrow $1000 dollars to buy a new Harry Potter wand. He has two options for borrowing: He can borrow the $1000 from the bank at an annual rate of 15% with daily compound interest. He doesn't pay back any of his loan until the end of the year (one full year). He can borrow the $1000 from Meghan, but she charges 20% interest (annual rate) but uses simple interest. He pays her back at the end of the year (12 months from now). Who should Dalton borrow from? Why?

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