Math 21 Earning and Spending Money - Ms. Harvey's Miller ...msharveyatmiller.weebly.com/uploads/4/8/4/0/48405249/book_3_student_-_interest.pdf6. Sanjay borrowed $7000 at a simple interest

Math 21 Earning and Spending Money

Book 3: Interest

Name: ______________________________

Start Date: ______________ Completion Date: ________________

Book 3: Math 21 Earning and Spending Money- Interest Edited February 2015

2

Year Overview:

Earning and Spending Money Home Travel Recreation and Wellness

1. Budget 2. Personal Banking 3. Interest 4. Consumer Credit 5. Major Purchases

6. Scale Drawings & Ratios

7. Area & Volume 8. Angles 9. Triangles 10. Slope & Elevation

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.

Suggested Timeframe: 6 Hours

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.


3

Contents Topic Overview.................................................................................................................. 2

Outcomes ....................................................................................................................... 2

Overlapping Outcomes in Budgeting .................................................................... 2

Theme Specific Outcomes ....................................................................................... 2

Interest ................................................................................................................................ 4

Check Your Skills ............................................................................................................ 4

3.1 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 ............................................................................................................ 9

3.1 Practice Your Skills ............................................................................................. 10

3.2 Understanding Compound Interest ....................................................................... 13

A. Calculating Interest on Interest ............................................................................ 13

B. Compounding Interest Grows Quickly ................................................................ 14

3.3 Why Borrow? .............................................................................................................. 15


3.4 Why Invest? ................................................................................................................ 18

3.4 Practice Your Skills – Investments .................................................................... 19

3.5 “Rule of 72” ................................................................................................................ 21


Learning Log .................................................................................................................... 24


4

Interest How would you like to earn some money while doing practically nothing? Interest can help you do that!

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 Your Skills 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

.033

.045

.07

.14

.159

Interest is the amount paid for the use of someone else’s money.


5

2. Solve for x for the following equations:a. 8 + 9 = x

b. 11 - 7 = x

c. 8 + x = 13

d. x + 5 = 19

e. 9 - x = 1

f. x - 14 = 6

g. 2(4) = x

h. 5x = 10

i. 20 = 4x

j. 10 ÷ 2 = x

k. 21 ÷ x = 7

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


6

Money is Not Free to Borrow!

People can always find a use for money, so it costs money to borrow money.

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?

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 http://www.elitemortgagechoice.com/


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!


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 ($1000 × 10%) x 2 Years = $200

That is how simple interest works. The borrower pays the same amount of interest every year.


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:

Principal = $1000

Interest rate = 10%

Time (in years) = 5 years

For Alex, his Interest will be:

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 = $1000 + $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 = 3000 × 0.05 × 4 I = $600


10

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?

Example: Donna borrowed $8999.00 over 3 years and paid $449.50 in simple interest over that time. What rate of interest did Donna pay?

Step 1: Divide $449.50 by 3 to find the amount of interest paid per year.

$449.50 ÷ 3 = $149.83

Step 2 : Divide the amount of interest paid by the principal

$149.83 ÷ $8999 = 0.016

Step 3: Change 0.016 to a percent

0.016 x 100 = 1.6%


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 $10 000 at 5% simple interest rate. What is the total amount Sally will have to pay back?


12

9. Trevor borrowed $10 000 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?


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.


14

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.

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) $1000.00 ($1000.00 × 10% = ) $100.00 $1100.00

1 $1100.00 ($1100.00 × 10% = ) $110.00 $1210.00

2 $1210.00 ($1210.00 × 10% = ) $121.00 $1331.00

3 $1331.00 ($1331.00 × 10% = ) $133.10 $1464.10

4 $1464.10 ($1464.10 × 10% = ) $146.41 $1610.51

5 $1610.51

So, after 5 Years Alex would have to pay back $1,610.51

Comparing this to Simple Interest over the same amount of time:


0 (Now) $1000.00 ($1000.00 × 10% = ) $100.00 $1100.00

1 $1100.00 ($1000.00 × 10% = ) $100.00 $1200.00

2 $1200.00 ($1000.00 × 10% = ) $100.00 $1300.00

3 $1300.00 ($1000.00 × 10% = ) $100.00 $1400.00

4 $1400.00 ($1000.00 × 10% = ) $100.00 $1500.00

5 $1500.00

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.


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.


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) $2000

1

2

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.


0 (now) $4000

1

2

3




17

3. Joe borrowed $8700 for 5 years at 17% compound interest rate.


0 (now)

1

2

3

4

5



4. Ricky borrowed $15 500 for 3 years at 8% compound interest rate.


0 (now)

1

2

3




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:


0 (Now) $1000.00 ($1000.00 × 15% = ) $150.00 $1150.00 1 $1150.00 ($1150.00 × 15% = ) $172.50 $1322.50 2 $1322.50 ($1322.50 × 15% = ) $198.38 $1520.88 3 $1520.88 ($1520.88 × 15% = ) $228.13 $1749.01 4 $1749.01 ($1749.01 × 15% = ) $262.35 $2011.36 5 $2011.36

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:

$3506.23 after 10 Years! For a 10 Year investment of $200 each year


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) $1000

1

2

a. What is the total value of the investment after 2 years?


2. Alice invested $6000 for 3 years at 10% compound interest rate. Calculate the cost of borrowing using the table below.


0 (now) $6000

1

2

3




20

3. Joe invested $9200 for 5 years at 17% compound interest rate. Calculate the cost of borrowing using the table below.


0 (now)

1

2

3

4

5




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.

72 ÷ 12 (interest rate) = 6

Your investment would take approximately 6 years to double.


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 $10 000 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 $10 000 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?


23

6. Ricky has $8000 that he will invest to double over 6 years to $16 000. To double his money, what interest rate will he have to invest his money at?

7. Heather has $22 000 that she will invest to double over 8 years to $44 000. 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?


24

Learning Log Date Starting Point Ending Point

Documents

Math 21 Earning and Spending Money - Ms. Harvey's Miller ...msharveyatmiller.weebly.com/uploads/4/8/4/0/48405249/book_3_student_-_interest.pdf6. Sanjay borrowed $7000 at a simple interest