Mathematics 9 Unit 10.3

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Unit 10 Section 3

Simple Interest and Compound interest

Warm-up:

1. Solve each problem.

a) What percent of 88 is 39?

b) 4 is what percent of 56?

c) 4 is what percent of 160?

d) What percent of 27 is 31?

e) What is 280% of 51?

f) 91% of 49 is what?

g) What is 0.340% of 157?

h) What is 2.9% of 65?

i) 97% of what is 87?

j) 147 is 95% of what?

k) 99% of what is 82.7?

l) 65 is 250% of what?

Notes:

The principles of interest occur throughout as you lend money, borrow money or save

money. Various financial institutions advertising their services: banks, trust companies,

credit unions. People deposit their money in accounts to earn interest or borrow money, in

which case, they will pay the bank the loan amount plus interest. The amount of money

deposited or borrowed is called the principle. The rate of interest varies with Canada’s

economy.

When interest is paid each time period on the original principal only, it is called simple

interest.

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The following formula is used to compute simple interest:

𝐼 = 𝑃 × 𝑟 × 𝑡

Interest($) Principle($) Annual Rate(in decimal) Length of time(year)

Examples:

1. Matthew borrowed $3000 at 12% for 2 years. Find the interest that he will be charged.

2. Eva put $500 into a savings account that pays simple interest. She withdrew the money

6 months later to go on a holiday. The bank gave her %517.50. What was the rate of

interest?

In today’s financial world, most financial institutions use compound interest to calculate

the interest payable. With compound interest the amount at the end of each time period

becomes the principal for the next period. With compound interest an interest is paid on

the interest.

Compound interest can be paid more than once a year. This is called the compounding

period.

Compounding periods

Annually _________________ Monthly _________________

Semi-annually _________________ Weekly _________________

Quarterly _________________ Daily _________________

3. Simon deposit $400 into an account that pays interest at the rate of 8% per year

compounded annually. How much will he have in his account at the end of the 2nd year?

Compare this with the amount he would have obtained if simple interest were used.

Period Starting Amount

Rate Interest Ending

Amount 0 400 1 400 2

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4. Sasha borrowed $750 from a bank that charges interest at the rate of 12% compounded

semi-annually. What amount is needed to pay off the loan at the end of one year?

Period Starting Amount

Rate Interest Ending

Amount 0 1 2

Summary: 1. Use simple interest to find the ending balance

a) $265 at 5.3% for 8 years

b) $24 000 at 9% for 4 years

2. Find the total value of the investment after the time given. a) $325 at 7% compounded quarterly

for 1 year

b) $$55 800 at 13% compounded semi-annually for 1.5 years

3. Clayton borrowed $2000 to buy a dirt bike. When he repaid the loan two years later, he was charged $510 interest. What rate of simple interest was used?

Homework:

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Exercises:

1. Use simple interest to find the ending balance.

a) $90 at 1% for 2 years b) $1000 at 14.5% for 5 years c) $33400 at 14% for 6 years d) $1400 at 3% for 7 years

2. Find the total value of investment after the time given.

a) $27 400 at 1% compounded quarterly for 1 years

b) $150 at 6% compounded daily for 1 week

c) $46 800 at 4% compounded monthly for 3 months

d) $4600 at 4% compounded semi-annually for 2 years

e) $510 at 15% compounded daily for 5 days

f) $26 700 at 7% compounded quarterly for 2 years.

g) $2900 at 6% compounded annually for 2 years

h) $60 000 at 10% compounded annually for 3 years

3. Ryan has $156.63 in his savings account, which pays simple interest at the rate of 7.5%.

How long will he have to let his deposit stay in his account for it to double?

4. Erin borrowed $1000 from a friend. She repaid the money in 12 monthly payments of

$92.79.

a) How much money did she repay in total?

b) How much interest did she pay her friend?

c) Find the annual interest rate of this loan. Give your answer to the nearest tenth of a

percent.

5. Dana borrows $2000 to set up her own apartment. The bank gave her the personal loan

charged interest at 12.5% per annum.

a) Find how much she would have to pay to clear the debt after 2 years if the interest is

compounded semi-annually.

b) In another institution, she could borrow the money at the same terms but

compounded annually. How much would she pay?

c) Which option is better? Justify your choice.

6. Noelle borrowed $6000 from her bank at 11% per annum compounded semi-annually.

She then invested the money in a business venture that paid her 12% per annum

compounded quarterly. How much money will she make at the end of one year?