3 07 - Simple Vs Compound Interest.pdf

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MCR 3U Simple & Compound Interest Date:

Simple Interest: only the money originally invested earns interest

How much interest would you earn on $1000 in an investment that pays 5% per annum on the starting balance?

Year Starting Balance

Balance that Interest is Calculated On

Interest Ending Balance

1 $1000 $1000 I = (1000)(.05)(1)

= $50 $1050

2 $1050 $1000 $50 $1100

3 $1100 $1000 $50 $1150

4 $1150 $1000 $50 $1200

5 $1200 $1000 $50 $1250

Compound Interest: the interest is reinvested at regular intervals. The interest is added to the principal to earn interest for the next interval of time, or compounding period.

How much interest would you earn on $1000 in an investment that pays 5% compounded annually?

Year Starting Balance

Balance that Interest is Calculated On

Interest

(I = Prt) Ending Balance

1 $1000 $1000 I = (1000)(.05)(1)

= $50 $1050

2 $1050 $1050 $52.50 $1102.50

3 $1102.50 $1102.50 $55.13 $1157.63

4 $1157.63 $1157.63 $57.88 $1215.51

5 $1215.51 $1215.51 $60.78 $1276.29

Using the tables above, what type of relationship exists between “year” and “ending balance”? Give a reason for your answer.

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MCR 3U Simple & Compound Interest – Examples Date:

Simple Interest:

t

I

=

Pr

I is the interest earned

P is the principal (amount invested) r is the interest rate (as a decimal) t is the time in years.

Compound Interest:

n

i

P

A

=

(

1

+

)

A is the future value of the investment P is the present value of the investment (principal)

i is the interest rate (per compounding period)

n is the total number of compounding periods Present Value: n i A P ) 1 ( +

= or PV = A(1+i)−n

PV is the present value of the investment (principal)

A is the future value of the investment i is the interest rate (per compounding period)

n is the total number of compounding periods

1. You invest $250 at 5% per annum at a bank that pays simple interest.

a) If you kept your money invested for 6 years, how much total simple interest would be earned? b) If you invested at double the interest rate would it double the total interest paid over 6 years? c) What annual interest rate would have been required for your investment to double in 6 years?

2. You invest $250 at 5% per annum at a bank that pays compound interest.

a) How much money would be in your bank account after 6 years if you did not withdraw any money? How much compound interest was earned?

b) If you invested at double the interest rate would it double the total interest paid over 6 years?

3. Claire is investing $10 000 in a RRSP. Plan A is a 9-year plan with an interest rate of 6% per annum, compounded semi-annually. Plan B is a 9-year plan with an interest rate of 5.95%, compounded monthly. Which plan should Claire choose? Justify your answer mathematically.

4. Brent would like to buy a $3 000 stereo in 3 years. How much must he invest today at 8% per annum compounded quarterly in order to be able to buy the stereo?

Answers:

1. a) $75

b) $150 therefore it doubles c) 16.7%

2. a) $335.02 in account, $85.02 interest earned

b) $442.89 in account, $192.89 interest earned therefore it more than doubles

3. Plan A $17024.33 Plan B $17060.43 Therefore choose Plan B

4. $2365.48

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GROUP A PROBLEMS

1. You invest $250 at 5% per annum at a bank that pays simple interest.

a) If you kept your money invested for 6 years, how much total simple interest would be earned?

b) If you invested at double the interest rate would it double the total interest paid over 6 years?

c) What annual interest rate would have been required for your investment to double in 6 years?

2. You invest $250 at 5% per annum at a bank that pays compound interest.

a) How much money would be in your bank account after 6 years if you did not withdraw any money? How much compound interest was earned?

b) If you invested at double the interest rate would it double the total interest paid over 6 years?

3. Econ Omy is investing $10 000 in a RRSP. Plan A is a 9-year plan with an interest rate of 6% per annum, compounded semi-annually. Plan B is a 9-year plan with an interest rate of 5.95%, compounded monthly. Which plan should Econ Omy choose? Justify your answer mathematically.

4. Break Thebank would like to buy a $3 000 stereo in 3 years. How much must he invest today at 8% per annum compounded quarterly in order to be able to buy the stereo?

Answers:

5. a) $75

b) $150 therefore it doubles c) 16.7%

6. a) $335.02 in account, $85.02 interest earned

b) $442.89 in account, $192.89 interest earned therefore it more than doubles

7. Plan A $17024.33 Plan B $17060.43 Therefore choose Plan B

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GROUP B PROBLEMS

1. You invest $350 at 7% per annum at a bank that pays simple interest.

a) If you kept your money invested for 5 years, how much total simple interest would be earned?

b) If you invested at double the interest rate would it double the total interest paid over 5 years?

c) What annual interest rate would have been required for your investment to double in 5 years?

2. You invest $350 at 7% per annum at a bank that pays compound interest.

a) How much money would be in your bank account after 5 years if you did not withdraw any money? How much compound interest was earned?

b) If you invested at double the interest rate would it double the total interest paid over 5 years?

3. Ann Ually is investing $5 000 in a RRSP. Plan A is a 10-year plan with an interest rate of 5% per annum, compounded semi-annually. Plan B is a 10-year plan with an interest rate of 4.75%, compounded monthly. Which plan should Sarah choose? Justify your answer mathematically.

4. Sem Ianually would like to buy a $2 000 mountain bike in 2 years. How much must he invest today at 7% per annum compounded semi-annually in order to be able to buy the mountain bike?

Answers:

1. a) $122.50

b) $245 therefore it doubles c) 20%

2. a) $490.89 in account, $140.89 interest earned

b) $673.90 in account, $323.90 interest earned therefore it more than doubles

3. Plan A $8193.08 Plan B $8032.54 Therefore choose Plan A

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GROUP C PROBLEMS

1. You invest $450 at 5% per annum at a bank that pays simple interest.

a) If you kept your money invested for 7 years, how much total simple interest would be earned?

b) If you invested at double the interest rate would it double the total interest paid over 7 years?

c) What annual interest rate would have been required for your investment to double in 7 years?

2. You invest $450 at 5% per annum at a bank that pays compound interest.

a) How much money would be in your bank account after 7 years if you did not withdraw any money? How much compound interest was earned?

b) If you invested at double the interest rate would it double the total interest paid over 7 years?

3. Big Spenda is investing $15 000 in a RRSP. Plan A is a 12-year plan with an interest rate of 8% per annum, compounded semi-annually. Plan B is a 12-year plan with an interest rate of 7.95%, compounded monthly. Which plan should Big Spenda choose? Justify your answer mathematically.

4. Jack would like to buy a $6 000 pre-owned truck in 3 years. How much must he invest today at 5% per annum compounded quarterly in order to be able to buy the truck?

Answers:

1. a) $157.50

b) $315 therefore it doubles c) 14.3%

2. a) $633.20 in account, $183.20 interest earned

b) $876.92 in account, $426.92 interest earned therefore it more than doubles

3. Plan A $38449.56 Plan B $38828.77 Therefore choose Plan B

4. $5169.05

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