Simple interest is one way of earning interest. Simple interest is governed by the equation:

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Day 1- Simple Interest

When money is borrow or invested is either owed or paid. When you borrow money you owe interest to the person you borrow from. When you invest money you owe earn interest. There are two types of interest and it depends on the account that you invest or borrow from how the interest works.

Simple interest is one way of earning interest. Simple interest is governed by the equation: 𝐼𝐼 = 𝑝𝑝𝑝𝑝𝑝𝑝

Where I= p= r= t=

Often the formula 𝐴𝐴 = 𝑃𝑃 + 𝐼𝐼 is used to show the total amount of the invested. Here I=

P= A=

Example 1: Jodi wants to borrow $1000. Her bank offers her the loan with 10% interest. Jodi agrees to repay the loan after one year.

• The interest rate is %/year.

• The principal of the loan is $ .

• The interest is $ .

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Example 2: If you took out a loan for $500 and had to pay it back with 15%/a interest, how much would you pay if you paid it back in 2 years?

The simple interest formula only works when the time value (t) is given in years. But sometimes a loan or an investment has a term given in days or months.

Example 3: Determine the value of “t” for:

a) 6 months b) 30 months c) 270 days

Example 4: Suppose you borrow $1000.00 that earns 8%/a simple interest. How much interest would be earned in each of the following time periods?

a) 1 year

b) 2 years

c) 6 months

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Example 5: Kim plans to invest $1500. Her bank offers her two different investment options. How much more money will Kym make in interest if she chooses option 2?

Example 6: A simple interest rate of 5%/a is offered on an investment of $1000. What is the accumulated amount after 55 days?

Vocabulary: interest: principal: accumulated amount: interest rate: term:

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Simple Interest Assignment

1. Match each variable with a value.

Variable Value

principal 280 d

interest 1.95%

rate $2000.00

time $29.92

2. Use the values above to calculate the interest earned. a) Is the interest that was given correct?

b) What is the amount at the end of the investment?

3. Saskia is a golf pro in Banff. She invested $1400 for 36 weeks in a GIC. She will use the money for new golf clubs, The interest rate is 1.75%/yr. How much will Saskia have to spend?

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4. Derain is a tour guide in the Rocky Mountains. He works about 8 months/year. Derain invests some of his salary while he works so he has money when he is not working.

Complete the chart

a) What is the total interest earned on all Derain’s investments?

5. Tamara is a broker’s assistant. She invested $750 for 6 months at an annual interest rate of 1.5%. She calculated the interest earned as $56.23. However, the paperwork showed she earned $5.63.

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Day 2- More Simple Interest

The simple interest formula can be rearranged to solve for other variables as well: 𝐼𝐼 = 𝑝𝑝𝑝𝑝𝑝𝑝

Example 1: Brady purchased a motorbike by borrowing $4450.00 from his grandfather which was to be repaid over 30 months. Calculate the annual simple interest rate if Brady repaid a total of $5135.25 to his grandfather.

Example 2: Sydney wants to earn $250 in interest so she’ll have enough to buy a used car. She puts $2000 into an account that earns 2.5% interest. How long will she need to leave her money in the account to earn $250 in interest?

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Example 3: Kole wants to move his savings account to a new bank that pays a better interest rate of 3.5% so that he can earn $100 in interest faster than at his old bank. If he moves $800 to the new bank, how long will it take for him to earn the $100 in interest?

Example 4: What happens to the amount of interest earned when : a) the principal and the term stay the same but the rate doubles?

b) the principal and the rate stay the same but the term doubles?

Example 5: How many months are needed to earn $103.13 in simple interest, on a principal of $2500 with an annual interest rate of 2.75%.

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More Simple Interest Assignment

1. Complete the chart. Round interest rates to the nearest hundredth of a percent, time to the nearest day and money to the nearest cent.

2. Dan is an RV service technician in Saskatchewan. He invested $3200 in a savings account 2 years ago. The interest rate was 0.8%/yr. He wants to spend the money fixing up an RV to sell. How much does Dan have to spend on the repairs?

3. Graham needs to purchase a line-striping machine for his painting business. He has saved $4200. He invested his savings in a 9 month term GIC for his new machine. At the end of the term, his GIC paid $51.26. What was the annual interest rate on Graham’s GIC? Round to the nearest hundredth of a percent.

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4. Kazuhiro invested $2000 of the money he earned working on a farm near Edmonton. He earned $14.96 in interest. He earned $14.96 in interest. The interest rate was 1.4%/yr. For how long did Kazuhiro invest the principal? Round up for the number of days.

5. Joti earned $48.74 in interest on money in a savings account. She invested her principal at an annual rate of 2.3% for 17 weeks. How much money did Joti invest?

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Day 3- Compound Interest

When we invest with a simple interest account the interest earned is put into a

account. When we invest with compound interest, the interest earned is .

Example 1: Shawn invested $12 000 five years ago, planning ahead for the down payment on a house. The investment earned compound interest at 2.3%/year, compounded annually. Now Scott is ready to withdraw the entire amount. How much will the withdrawal be?

Year _{(amount at start of year)} Principal Simple Interest _{I = Prt} Amount at End of Year A = _{P + I}

1 $12 000

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What is compound interest? • • • Principal Interest Earned Principal Interest Earned

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BUT THAT IS CRAZY LONG! SO……

𝐴𝐴 = 𝑃𝑃(1 +_𝑛𝑛)𝑝𝑝 𝑛𝑛𝑛𝑛

Example 1 AGAIN: Shawn invested $12 000 five years ago, planning ahead for the down payment on a house. The investment earned compound interest at 2.3%/year, compounded annually. Now Scott is ready to withdraw the entire amount. How much will the withdrawal be?

Compound interest may be calculated more than once a year (annual). This means that the number of compounding periods (n) may not always be 1. Below are typical numbers of compounding periods. How many times per year will the interest be calculated using these terms?

Where: A = accumulated amount P = principal r = interest rate n = # of compounding periods t = time

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Since the number of compounding periods doesn’t always have to be 1, in other words the interest rate is not always annual, we have to adjust the interest rate to per compounding period.

Example 3: Fill in the table below, adjusting for the number of compounding periods.

Annual Interest

Rate Compounding Period Time

r

n

tn

Example 4: Bailey deposits $2400.00 into a two-year term deposit which earns 6.5%/year compounded quarterly. Determine the accumulated amount at the end of the term.

Since the interest is added onto the principal after every compounding period, to find the amount of interest earned, we need to subtract the original principal.

Example 4 AGAIN: Bailey deposits $2400.00 into a two-year term deposit which earns 6.5%/year compounded quarterly. Determine the interest earned.

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Compound Interest Assignment

1. Islay is a jeweler in Fort McMurray.

• Islay uses Canadian diamonds mined in Lac de Gras.

• She makes an annual trip to Yellowknife to buy stock at wholesale prices.

• To save money for her next trip, she bought a $12 000 GIC for 1 yr. It paid 2.1%/yr. How much money will Islay have after 1 yr?

2. Darby is a cabinetmaker in Watson Lake. She used $1500 profit from the sale of a cabinet to buy a GIC. It is a 3 yr GIC with an interest rate of 2.2%/yr, compounded annually.

a) How much money will Darby have at the end of the 3 yr?

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3. Henny is a plumber in Kamloops. She installed 17 toilets in a new townhouse complex. • She charged $50 per toilet installed.

• She invested the money for 2 years into a savings account. • The account paid 1.3%/yr, compounded annually.

How much will Henny have after 2 years?

4. Suppose you have these choices for saving money. Both accounts have the same interest rate. Which would you choose? Explain.

• One account uses simple interest.

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Day 4- More Compound Interest

Simple interest and compound interest differ by:

Which method of interest grows faster? Why?

Example 1: Michael recently inherited $25,000 from his late Uncle Jake and would like to invest the money into a GIC (Guaranteed Investment Certificate). Which is the better investment and by how much?

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Example 2: Tameka deposits $4000.00 into an investment account that offers 3.00% interest per annum, compounded daily.

a) How much will her investment be worth after 3 years?

b) How much will it be worth after 10 years?

Example 3: Roger has a $1000.00 investment that offers an interest rate of 2.50% per annum,

compounded monthly. If he invests it for 5 years, how much will the investment be worth at the end of the term?

Example 4: Calculate the final value of an investment of $5000.00 over a term of 10 years and a rate of 2.60% at the following compounding periods:

a) annually b) quarterly

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More Compound Interest Assignment

1. Pearl, a refrigeration mechanic, wants to open her own shop in 3 years. • She needs $20 000 down payment to start the business.

• She plans to invest at a rate of 3.9%/yr, compounded annually. How much does Pearl need to invest now to have $20 000 in 3 years?

2. Mishak plans on retiring from his job as a gas fitter in 25 years. This year, he invests $10 000 in his retirement plan at 3.2%.yr. Will Mishak double his investment before he retires?

3. Theresa is investing $7100 in a 3 year savings plan. It pays 3.15%/yr, compounded semi-annually. How much money will Theresa have after 3 years?

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Day 6- Rule of 72

A common question regarding investments is how long will it take for the investment to double. For simple interest:

Example 1: $100 is invested at 5%/a interest. How long will it take to double?

For compound interest we use the “Rule of 72”. The time it will take an investment (or debt) to double in value at a given interest rate using compounding interest.

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𝐼𝐼𝑛𝑛𝑝𝑝𝐼𝐼𝑝𝑝𝐼𝐼𝐼𝐼𝑝𝑝 𝑅𝑅𝑅𝑅𝑝𝑝𝐼𝐼 = # 𝑜𝑜𝑜𝑜 𝑌𝑌𝐼𝐼𝑅𝑅𝑝𝑝𝐼𝐼 𝑝𝑝𝑜𝑜 𝑑𝑑𝑜𝑜𝑑𝑑𝑑𝑑𝑑𝑑𝐼𝐼

Example 2: Use the rule of 72, if Doug invests $400 at 3% compounded annually. a) How long will it take him to double his money?

b) Confirm that the answer from a) would double Doug’s investment.

Example 3: Use the rule of 72 to figure out how many months, it will take Karl to double his $2000 if it is compounded monthly at 8%.

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Rule of 72 Assignment

1. Susie is a landscaper. She leases a truck for her business. She plans to buy out the lease in 6 years. She has half the money now. At what interest rate, compounded annually, does Susie need to invest now in order to double her money in 6 years?

Mid Unit Review

2. James is an electrical contractor who needs to buy some new equipment for his business. He invests $500 into a simple interest savings account that pays 2.5%/yr, for 18 months. How much will James have to spend on his equipment after 18 months?

3. Cassie needs to have an extra $100 in 26 weeks. How much would she have to invest today in a simple interest savings account that paid an annual rate of 1.8% in order to have the additional $100 in 26 weeks?

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4. Show the steps required to isolate t in the formula I=prt.

5. Justin is offered three different savings accounts to invest $4000. He intends to use the money to purchase tools that he needs in order to expand his plumbing business. If he wants to expand in three years, which account would give him the most money to do so?

Account 1 3%/a compounded semiannually; $10 annual fee. Account 2 2.4%/a compounded semiannually; $30 annual fee. Account 3 3.5%/a compounded semiannually; No annual fee.

6. Rufus invested $12000 at 8%/a compounded quarterly for 15 years. How much interest did he earn after 15 years?

7. Explain why investing $100 in a savings account at 3%/yr compounded annually for three years is better than investing it in an account paying 3% simple interest for three years.