Math 21 Earning and Spending Money. Book 3: Interest. Teacher Version Assessments and Answers Included

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1 Math 21 Earning and Spending Money Book 3: Interest Teacher Version Assessments and Answers Included

2 Year Overview: Earning and Spending Money 1. Budget 2. Personal Banking 3. Interest 4. Consumer Credit 5. Major Purchases Home 6. Scale Drawings & Ratios 7. Area & Volume 8. Angles 9. Triangles 10. Slope & Elevation Travel and Transportation Recreation and Wellness 11. Travel Project 12. Puzzles & Games 13. Understanding Statistics 14. Budgeting Recreation Topic Overview You may have already entered the workforce and have some knowledge about earning and spending money. The intent of this theme is to help you be aware of financial decision making that you face. In this section, you will learn about the cost of borrowing money as well as the benefit to investing it. Outcomes Overlapping Outcomes in Budgeting M21.1 Extend and apply understanding of the preservation of equality by solving problems that involve the manipulation and application of formulae within home, money, recreation, and travel themes. Theme Specific Outcomes M21.9 Demonstrate understanding of financial institution services. 2

3 Contents Topic Overview... 2 Outcomes... 2 Overlapping Outcomes in Budgeting... 2 Theme Specific Outcomes... 2 Interest... 4 Check What You Know Understanding Simple Interest... 6 A. How Much does it Cost to Borrow Money?... 6 B. Terms to Understand Interest... 8 C. Simple Interest Loans of More Than One Year... 8 Simple Interest Practice Your Skills Understanding Compound Interest A. Calculating Interest on Interest B. Compounding Interest Grows Quickly Why Borrow? Practice Your Skills Why Invest? Practice Your Skills Investments Rule of Practice Your Skills Student Evaluation Learning Log Show What You Know - Comparing Simple & Compound Interest Answers

4 Interest How would you like to earn some money while doing practically nothing? Interest can help you do that! Interest is the amount paid for the use of someone else s money. Two things to consider are the interest rate, or percent, and the amount of time that the money is being borrowed for. The higher the rate and the longer the time, the more interest is charged. Check What You Know 1. Please perform the following conversions: a) Change from percent to decimal percent decimal 3% 4.5% 6.3% 18% 19.8% b) Change from decimal to percent percent decimal Solve for x for the following equations: a = x c. 8 + x = 13 b = x d. x + 5 = 19 4

5 e. 9 - x = 1 i. 20 = 4x f. x - 14 = 6 j = x g. 2(4) = x k. 21 x = 7 h. 5x = 10 l. 9 = x 8 3. Given the equation x = yz, a. Solve for y b. Solve for z 4. Given the equation de = f, a. Solve for d b. Solve for e 5

6 3.1 Understanding Simple Interest Interest can be a good thing for the person who earns it, but it is not very nice for the person who has to pay it. For example, Investing Money: o if you deposit some of your money in the bank, the bank pays you interest since you let them use your money. You end up with more money than you deposited in the first place. Borrowing Money: o if you borrow money from the bank, you have to pay interest to the bank since they let you use their money. You end up repaying more than you borrowed in the first place. A. How Much does it Cost to Borrow Money? Money is Not Free to Borrow! People can always find a use for money, so it costs money to borrow money. Interest is charged at a certain rate which is a %/given time. Usually, the time that a rate is given for is one year. Even when a rate is quoted over 2 or more years, the interest rate is for one year, and interest is calculated per year. From 6

7 Example: Borrowing $1000 from the Bank Alex wants to borrow $1000. The local bank says 10% interest. To borrow the $1000 for 1 year, Alex s cost will be: $1000 x 10% = $100 In this case, the interest is $100 and the interest rate is 10%. You may hear people say 10% interest without saying rate. Alex is responsible for paying back the original $1000 after 1 year as well as the interest. Alex s total payback next year will be: $1000 original principal + $100 interest = $1100 paid back This is the idea of Interest... paying for the use of the money. Note: This showed you a full year loan, but banks often want you to pay back the loan in small monthly amounts, They may charge extra financing fees as well! 7

8 B. Terms to Understand Interest There are special words used when borrowing money, as shown here: Alex is the Borrower, the Bank is the Lender The Principal of the Loan is $1000 The Interest is $100 The important part of the word "Interest" is Inter- meaning between (you see inter- in words like interior and interval), because the interest happens between the start and end of the loan. C. Simple Interest Loans of More Than One Year What if Alex wanted to borrow the money for 2 Years? If the bank charges "Simple Interest" then Alex just pays another 10% for the extra year. Alex pays Interest of ($ %) x 2 Years = $200 That is how simple interest works. The borrower pays the same amount of interest every year. 8

9 Simple Interest Example: How much would Alex have to pay back if he borrowed $1000 for 5 years at an interest rate of 10%? Interest = Principal x Interest Rate x Time (in years) The information for Alex s loan is: For Alex, his Interest will be: Principal = $1000 Interest rate = 10% Time (in years) = 5 years Interest = $1000 x $10%/Year x 5 Years Interest = $500 To find out the total amount he must pay back: Total Pay back = Principal + Interest Total Pay back = $ $500 Total Pay Back = $1500 If you look closely, you can see the Interest Formula in the example above: I = Prt I = interest P = amount borrowed (called "Principal") r = interest rate t = time Example : Jan borrowed $3,000 for 4 Years at 5% interest rate, how much interest will she have to pay? I = Prt I = $3000 5% 4 years I = I = $600 9

10 Example: Donna borrowed $ over 3 years and paid $ in simple interest over that time. What rate of interest did Donna pay? Step 1: Divide $ by 3 to find the amount of interest paid per year. $ = $ Step 2 : Divide the amount of interest paid by the principal $ $8999 = Step 3: Change to a percent x 100 = 1.6% 3.1 Practice Your Skills Ask Your Teacher how many of the following questions you should complete. 1. Jerry borrowed $4000 for 5 years at 6% simple interest rate. How much interest is that? 2. Julie borrowed $3500 for 3 years at 7.5% simple interest rate. How much interest is that? 3. Dan borrowed $2000 for 6 months at 12% annual simple interest rate. How much interest is that? 10

11 4. Jenna borrowed $5000 for 3 years and had to pay $1,350 simple interest at the end of that time. What rate of interest did she pay? 5. Sam borrowed $4500 for 2 years and had to pay $630 simple interest at the end of that time. What rate of interest did Sam pay? 6. Sanjay borrowed $7000 at a simple interest rate of 3% per year. After a certain number of years he had paid $840 in interest altogether. How many years was that? 7. Sarina borrowed $5800 at a simple interest rate of 7½% per year. After a certain number of years she had paid $1305 in interest altogether. How many years was that? 8. Sally borrowed $ at 5% simple interest rate. What is the total amount Sally will have to pay back? 11

12 9. Trevor borrowed $ at 13% simple interest rate. What is the total amount Trevor will have to pay back? 10. Molly borrowed $5000 at 19% simple interest rate. What is the total amount Molly will have to pay back? 12

13 3.2 Understanding Compound Interest A. Calculating Interest on Interest When a loan stretches out for more than one year, a bank will often calculate interest as compounding interest. This is like a bank saying "What if you paid me everything back after one year, and then I loaned it to you again... I would be loaning you $1100 for the second year! And Alex would pay $110 interest in the second year, not just $100. Because Alex is paying 10% on $1100 not just $1000 This is the normal way of calculating interest. It is called compound interest. With compounding interest you work out the interest for the first period, add it the total, and then calculate the interest for the next period, and so on..., like this: If you think about it... it is like paying interest on interest. Because after a year Alex owed $100 interest, the Bank thinks of that as another loan and charges interest on it, too. 13

14 B. Compounding Interest Grows Quickly After a few years it can get really large. This is what happens on a 5 Year Loan: Year Loan at Start Interest Loan at End 0 (Now) $ ($ % = ) $ $ $ ($ % = ) $ $ $ ($ % = ) $ $ $ ($ % = ) $ $ $ ($ % = ) $ $ $ So, after 5 Years Alex would have to pay back $1, Comparing this to Simple Interest over the same amount of time: Year Loan at Start Interest Loan at End 0 (Now) $ ($ % = ) $ $ $ ($ % = ) $ $ $ ($ % = ) $ $ $ ($ % = ) $ $ $ ($ % = ) $ $ $ In Summary: To calculate compound interest, work out the interest for the first period, add it on, and then calculate the interest for the next period, etc. What is Year 0? Year 0 is the year that starts with the "Birth" of the Loan, and ends just before the 1st Birthday. Just like when a baby is born its age is zero, and will not be 1 year old until the first birthday. So the start of Year 1 is the "1st Birthday". And we can know the start of Year 5 is exactly when the loan is 5 Years Old. 14

15 3.3 Why Borrow? Sometimes, you need to borrow something you want or need and don t have enough cash to purchase it. As well, sometimes businesses use borrowed money to invest in their business so that they can make more money. Compound Interest Example: A Chicken Business A business owner borrows $1000 to start a chicken business in order to buy chicks, chicken food, and materials to build a chicken coop. a year later, the owner sells grown chickens for $1200. The loan had an interest rate of 10%. What would the owner s profit be? The interest on the loan would be: Interest = Principal x Interest Rate x Time (in years) Interest = $1000 x 10%/year x 1 year Interest = $100 The total payback on to the bank would be: Total Loan = Principal + Interest Total Loan = $1000+ $100 Total Loan = $1100 The owner needed to pay back $1100, and sold the chicks for $1200. This means that the profit was $100. Loan interest is a cost that businesses need to be aware of so that they price their goods and services high enough to make a profit. If the chicken business owner had sold his chicks for less than $1100, he would not have made enough to pay back his loan in full. 15

16 3.3 Practice Your Skills Ask Your Teacher how many of the following questions you should complete. 1. Alex borrowed $2000 for 2 years at 5% compound interest rate. Year Loan at start Interest Loan at end 0 (now) $ a. What is the total amount to be repaid? b. How much interest is paid? 2. Alice borrowed $4000 for 3 years at 10% compound interest rate. Year Loan at start Interest Loan at end 0 (now) $ a. What is the total amount to be repaid? b. How much interest is paid? 16

17 3. Joe borrowed $8700 for 5 years at 17% compound interest rate. Year Loan at start Interest Loan at end 0 (now) a. What is the total amount to be repaid? b. How much interest is paid? 4. Ricky borrowed $ for 3 years at 8% compound interest rate. Year Loan at start Interest Loan at end 0 (now) a. What is the total amount to be repaid? b. How much interest is paid? 17

18 3.4 Why Invest? Compound Interest can work for you! An Investment is where you put your money where it could grow, such as a bank, or a business. If you invest your money at a good interest rate it can grow very nicely. This is what 15% interest on $1000 can do: Year Loan at Start Interest Loan at End 0 (Now) $ ($ % = ) $ $ $ ($ % = ) $ $ $ ($ % = ) $ $ $ ($ % = ) $ $ $ ($ % = ) $ $ $ It more than doubles in 5 Years! Of course, you would be lucky to find a safe investment at 15%... but it does show you the power of compounding. The graph of your investment would look like this: Maybe you don't have $1000, but if you could save $200 every year for 10 Years at 10% interest, this is how your money would grow: $ after 10 Years! For a 10 Year investment of $200 each year 18

19 3.4 Practice Your Skills Investments Ask your teacher how many of the following questions you should complete. 1. Alex invested $1000 for 2 years at 5% compound interest rate. Calculate the cost of borrowing using the table below. Year Investment at start Interest Loan at end 0 (now) $ a. What is the total value of the investment after 2 years? b. How much interest is paid? 2. Alice invested $6000 for 3 years at 10% compound interest rate. Calculate the cost of borrowing using the table below. Year Investment at start Interest Loan at end 0 (now) $ a. What is the total value of the investment after 3 years? b. How much interest is paid? 19

20 3. Joe invested $9200 for 5 years at 17% compound interest rate. Calculate the cost of borrowing using the table below. Year Investment at start Interest Loan at end 0 (now) a. What is the total value of the investment after 5 years? b. How much interest is paid? 20

21 3.5 Rule of 72 Do you know the Rule of 72? It's an easy way to calculate just how long it's going to take for your invested money to double. Just take the number 72 and divide it by the interest rate you hope to earn. 72 Interest rate = Estimated years to double That number gives you the approximate number of years it will take for your investment to double. Example: How long will it take your investment to double at an interest rate of 12%? divide 12 into 72 and you get six years (interest rate) = 6 Your investment would take approximately 6 years to double. 21

22 3.5 Practice Your Skills Ask your teacher how many of the following questions you should complete. Using the Rule of 72, answer the following questions. Please show your work. Round to the nearest year. 1. Doug invested $2500 earning 5% interest. How long will it take to double Doug s investment? 2. Steve invested $5500 earning 10% interest. How long will it take to double Steve s investment? 3. Randy invested $8000 earning 6.5% interest. How long will it take to double Randy s investment? 4. Jim invested $ earning 3.5% interest. How long will it take to double Jim s investment? 5. Jacob has $5000 that he has saved from doing odd jobs around the neighborhood. When he graduates from college in four years, he would like to have $ to use as a down payment on a new car. If Jacob is going to realize his dream, what interest rate will he have to invest his money at? 22

23 6. Ricky has $8000 that he will invest to double over 6 years to $ To double his money, what interest rate will he have to invest his money at? 7. Heather has $ that she will invest to double over 8 years to $ To double her money, what interest rate will he have to invest his money at? 8. Rhonda is 22 years old and would like to invest $2000 earning 7.5% interest. How many times will Rhonda s investment double before she draws it out at age 70? 23

24 Student Evaluation Insufficient Evidence (IE) Developing (D) Growing (G) Proficient (P) Exceptional (E) Student has not demonstrated the criteria below. Student has rarely demonstrated the criteria below. Student has inconsistently demonstrated the criteria below. Student has consistently demonstrated the criteria below. Student has consistently demonstrated the criteria below. In addition they have shown their understanding in novel situations or at a higher level of thinking than what is expected by the criteria. Proficient Level Criteria IE D G P E M21.1 Extend and apply understanding of the preservation of equality by solving problems that involve the manipulation and application of formulae within home, money, recreation, and travel themes. [WA10.1 and WA20.1] a. I can verify whether given forms of the same formula are equivalent and justify the conclusion. b. I can describe, using examples, how a given formula is used with money c. I can create, solve, and verify the reasonableness of solutions to questions that involve a formula. e. I can solve, with or without the use of technology, questions that involve the application of a formula that: does not require manipulation does require manipulation. Proficient Level Criteria IE D G P E M21.9 Demonstrate understanding of financial institution services. [WA20.7 and WA20.8] i. I can calculate simple interest, given three of the four values in the formula I=Prt and explain the reasoning. j. I can calculate compound interest using a formula. k. I can explain what is the same and what is different about simple interest and compound interest. l. I can explain, using examples what happens when you change different factors on compound interest (e.g., different amortization periods, interest rates, compounding periods, and terms). m. I can estimate, using the Rule of 72, the time required for a given investment to double in value and explain the reasoning. 24

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26 Learning Log Date Starting Point Ending Point 26

27 Show What You Know - Comparing Simple & Compound Interest 1. Julian borrowed $2000 for 2 years at 5% interest rate. Calculate the cost of borrowing for both simple interest and compound interest. Simple Interest: Compound Interest: Year Loan at start Interest Loan at end 0 (now) $200 $100 $ $2100 $105 $ $2205 Which type of interest is better for Julian? 27

28 2. Kelly invested $9900 for 5 years at 15% interest rate. Calculate the cost of borrowing for both simple interest and compound interest. Simple Interest: Compound Interest: Year Investment at start Interest Investment at end 0 (now) Which type of interest is better for Kelly? 28

29 3. Harry invested $ for 3 years at 8% interest rate. a. Calculate the cost of borrowing (the interest paid) for both simple and compound interest. b. Which type of interest is better for Harry? 4. Jane borrowed $ for 6 years at 5% interest rate. a. Calculate the cost of borrowing for both simple and compound interest. b. Which type of interest is better for Jane? 29

30 Answers Check What You Know 1. a) b) percent decimal 3% % % % % percent decimal 3.3% %.045 7%.07 14% % a. x = 17 b. x = 4 c. x = 5 d. x = 14 e. x = 8 f. x = 20 g. x = 8 h. x = 2 i. x = 5 j. x = 5 k. x = 3 l. x = a. y = x/y b. z = x/y 4. a. d=f/e b. e = f/d 30

31 3.1 Practice Your Skills 1. $ $ $ % 5. 7% $ $ $ Practice Your Skills 1. Year Loan at start Interest Loan at end 0 (now) $2000 $100 $ $2100 $105 $ $2205 a. $2205 b. $ Alice borrowed $4,000 for 3 years at 10% compound interest rate. Year Loan at start Interest Loan at end 0 (now) $4000 $400 $ $4400 $440 $ $4840 $484 $ $5324 a. $5324 b. $

32 3. Joe borrowed $8,700 for 5 years at 17% compound interest rate. Year Loan at start Interest Loan at end 0 (now) $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ a. $ b. $ Ricky borrowed $ for 3 years at 8% compound interest rate. Year Loan at start Interest Loan at end 0 (now) $ $ $ $ $ $ $ $ $ $ a. $ b. $

33 3.3 Practice Your Skills Investments 1. Alex invested $1000 for 2 years at 5% compound interest rate. Year Investment at start Interest Investment at end 0 (now) $1000 $50 $ $1050 $52.50 $ $ a. $ b. $ Alice invested $6 000 for 3 years at 10% compound interest rate. Year Investment at start Interest Investment at end 0 (now) $6000 $600 $ $6600 $660 $ $7260 $726 $ $7986 a. $7 986 b. $ Joe invested $9 200 for 5 years at 17% compound interest rate. Year Investment at start Interest Investment at end 0 (now) $9200 $1564 $ $ $ $ $ $ $ $ $ $ $ $ $ $ a. $ b. $

34 3.4. Practice Your Skills years 2. 7 years years years % 6. 12% 7. 9 % 8. It will have doubled 5 times. Show What You Know - Comparing Simple & Compound Interest 1. Julian borrowed $2000 for 2 years at 5% interest rate. Calculate the cost of borrowing for both simple interest and compound interest. Simple Interest: $200 Compound Interest: Year Loan at start Interest Loan at end 0 (now) $2000 $100 $ $2100 $105 $ $2205 Which type of interest is better for Julian? The cost of borrowing is less with simple interest. 34

35 2. Kelly invested $9,900 for 5 years at 15% interest rate. Calculate the cost of borrowing for both simple interest and compound interest. Simple Interest: $7 425 Compound Interest: Year Investment at start Interest Investment at end 0 (now) $9900 $ 1485 $ $ $ $ $ $ $ $ $ $ $ $ $ $ Which type of interest is better for Kelly? The cost of borrowing is less with simple interest. 35

36 3. Harry invested $ for 3 years at 8% interest rate. a. Calculate the cost of borrowing for both simple and compound interest. Simple: $2400 Compound: $ b. Which type of interest is better for Harry? Simple interest 4. Jane borrowed $ for 6 years at 5% interest rate. a. Calculate the cost of borrowing for both simple and compound interest. Simple: $ Compound: $ b. Which type of interest is better for Jane? Simple interest 36