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1.1
Simple Interest
YOU WILL NEED
• calculator
• graph paper
• ruler
Keep in Mind
Simple interest is determined only on the principal of an investment.
• The amount of simple interest earned on an investment can be determined
using the formula I 5 Prt.
TIP
• I is the interest.
• To determine the future value or amount of an investment that earns
simple interest, use the formula A 5 P 1 Prt or A 5 P(1 1 rt).
• P is the principal.
An interest rate is assumed to be annual, or per annum (per year).
• t is the time in years.
Investments are described by giving
• the interest rate;
• r is the annual interest
rate (as a decimal).
• A is the future value
or amount of the
investment.
• how and when interest is calculated, for example, simple interest calculated
annually or monthly; and
• the term: how long the money is invested.
Example 1
Nathan invested in a $3000 guaranteed investment certificate (GIC) at 1.5%
simple interest, paid annually, with a term of 5 years.
How much interest will accumulate over the term of Nathan’s investment?
What is the future value of his investment at maturity?
Solution
Step 1. I wanted to determine the accumulated interest, so I used the formula
I 5 Prt. I identified the terms I knew.
• The principal is $3000: P 5 3000
• The interest rate is 1.5% per annum: r 5 0.015
• The time is 5 years: t 5 5
Step 2. I substituted the values into the formula and calculated.
I 5 Prt
I 5 (3000)(0.015)(5)
I 5 225
Nathan will accumulate $225 in interest over 5 years.
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Simple Interest
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TIP
To convert a percent to a
decimal, first think of the
percent as a fraction. For
example,
1.5
1.5% 5
, or 0.015.
100
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Step 3. I know that the future value is the value of the investment at the end of the
5 years. To determine the future value, A, I added the principal and the accumulated
interest.
A5P1I
A 5 3000 1 225
A 5 3225
The future value is $3225.
Example 2
Caitlin is a co-op student. She invested her work-term earnings of $10 000 at
4% simple interest, paid annually. She intends to use the money in a few years to
take a dream vacation with a friend.
How long will the investment take to grow to a future value of $12 000?
Determine Caitlin’s rate of return.
Solution
Step 1. I wanted to determine the number of years it will take $10 000 to grow to
$12 000. I decided to use the formula A 5 P 1 Prt and solve for t.
• The principal is $10 000: P 5 10 000
• The rate of interest is 4% per annum: r 5 0.04
• The future value is $12 000: A 5 12 000
Step 2. I substituted and then solved for t.
A 5 P 1 Prt
12 000 5 10 000 1 (10 000)(0.04)t
2000 5 400t
2000
5t
400
55t
The value of the investment will be $12 000 in 5 years.
Step 3. I calculated the interest earned.
Interest earned: future value 2 principal 5 $12 000 2 $10 000, or $2000
Step 4. I determined the rate of return.
TIP
interest earned
Rate of return 5
amount invested
Rate of return 5
2000
10 000
Determine the rate of
return as the ratio of
money earned to the
amount of money invested.
Rate of return 5 0.2
The rate of return is 20% over 5 years.
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Practice
1. Rahim invests $250 at 3.5% simple interest for 3 years.
a) Determine the interest earned on Rahim’s investment.
b) Determine the future value of Rahim’s investment.
c) Determine Rahim’s rate of return.
2. Paula invested her summer earnings of $3000 at 2.4% simple interest, paid
annually. She will use the money in a few years to help with university expenses.
a) How long will it take for the future value of the investment to grow to
$3500? Round your answer to the nearest year.
TIP
For the rate of return, use
the actual value at the
end of the year when the
investment is worth at least
$3500, not the desired
value of exactly $3500.
b) Determine Paula’s rate of return, to the nearest tenth of a percent.
3. When Jeremy was born, his grandmother invested $1500 at 3% simple
interest, paid annually. The money is to be used for school expenses.
a) How long will it take for the future value of the investment to grow to
$2000? Round your answer up to the nearest year.
TIP
Round the number of years
up in this case, because
interest is not paid until the
end of each year.
b) Determine the rate of return, to the nearest tenth of a percent.
4. A principal of $800 000 is invested at 3.4% simple interest, paid annually, for
5 years. What is the rate of return?
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5. A principal of $16 500 is invested at simple interest for 15 years and grows to
a future value of $22 000.
a) Determine the interest rate. Round your answer to the nearest tenth of
a percent.
TIP
Interest rates are almost
always quoted per year,
but sometimes they are
calculated more frequently.
b) Determine the rate of return, to the nearest tenth of a percent.
MULTIPLE CHOICE
6. $270 is invested at 1.25% simple interest for 6 years. Interest is paid weekly.
Determine the interest earned.
A. $202.50
B. $3.38
C. $20.25
D. $270.25
7. Audrey invested $60 000 at 1.9% simple interest. At the investment’s
maturity, its value was $62 280. For how long was the money invested, and
what was the rate of return?
A. 1 year, 1.9%
B. 2 years, 1.9%
C. 1 year, 3.8%
D. 2 years, 3.8%
8. Aiden invested $435 at simple interest for 3 years. At the investment’s
maturity, its value was $572.03. What was the rate of interest, and what was
the rate of return?
A. 1.05%, 20%
B. 20%, 10.5%
C. 10.5%, 20%
D. 12%, 15%
WRITTEN RESPONSE
9. Amelia deposits $500 into a savings account that earns 3% simple interest,
for 2 years. On the same day, her brother Caleb deposits $200 into a savings
account that earns 5% simple interest, for 3 years. Who will earn more
interest? Who has the greater rate of return? Provide a complete solution.
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