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 UNIT 12  :  MATHEMATICS OF INVESTMENT

 LESSON 1: SIMPLE AND COMPOUND INTEREST HOMEWORK QUESTIONS

 

Quick Review:

Simple Interest:

When you borrow or invest money, interest is paid or earned.  If the interest is calculated only on the money originally invested, it is called simple interest.

Text Box: I  = interest due or earned
p = principal [amount borrowed                                
        or invested]
t  = time in years
r  = yearly interest rate as a decimal
A = amount repayable or accumulated
Text Box: Formulas:
 I = prt
A = p(1+ rt)
 

 

 


                                                                                                                       

 

 

 

 

 

Compound Interest:

If interest is calculated at the end of each year (or interest period) and added on at this point, then this is called compound interest.

Text Box: P = principal [amount borrowed                                
       or invested]
n = number of interest periods
i  = interest rate per interest period as  
      as a decimal
A = accumulated amount (due or payable)
Text Box: Formula:
 A = P(1+ i)n
 

 

 


                                                                                                                       

 

 

 

 

 

Homework Questions: (see solutions below)

1. Calculate the amount for each loan.

a)  $2000 for 6 years at 4%/a, compounded semi-annually.

b) $12 000 for 10 years at 5.35%/a, compounded annually.

c) $25 000 for 8 years at 4.5%/a, compounded quarterly.

d) $50 000 for 4 years at 4.25%/a, compounded monthly.

e) $44 000 for 6 ½ years at 5.5%/a, compounded semi-annually.

 

2.  Calculate the amount for each term deposit and the interest paid at the end of the term.

a) $17 000 for 3 years at 4.4%/a, compounded quarterly.

b) $7500 for 5 years at 4%/a, compounded semi-annually.

c) $ 24 000 for 6 years at 5.5%/a, compounded monthly.

d) $ 14 000 for 7 years at 4.4%/a, compounded daily.

 

3.  On the birth of their grandson, Carole and John invested $5000 for his education.  If the investment pays 8%/a, compounded monthly, how much will be available for his education when he turns 18?

 

4. a)  Barry wins $250 000 in the lottery.  If he invest $200 000 of it for 3 years at 6%/a, compounded quarterly, how much interest will he have earned?

   

5.  Nancy invested $2000 from his summer job in a Guaranteed Investment Certificate (GIC).  He is saving to go to university in 3 years.  How much will he have if interest is 6.54%/a, compounded monthly?

 

6.  The population of Cardiff is now 125 000.  If it grows at a rate of 1.5%/a, what will it’s population be in 25 years?

 

7.  If Ontario’s energy consumption is 650 megawatts in the year 2000 and is projected to grow at a rate of 5%/a, what will the consumption be in year 2050 ?

 

8.  Raja won $100 000 in the lottery.  He invested half of it in a GIC which pays 5.6%/a, compounded quarterly and the rest in a bond that pays 4.8%/a compounded semi-annually.  How much will he have in 10 years?

 

9.  Compare the following investments.  Which is better?

a)  $20 000 invested for 6 years at 5%/a, compounded semi-annually.

a)  $20 000 invested for 6 years at 5%/a, compounded monthly.

a)  $20 000 invested for 6 years at 5%/a, compounded daily.

 

Solutions:

1. Calculate the amount for each loan.

a)  $2000 for 6 years at 4%/a, compounded semi-annually.

b) $12 000 for 10 years at 5.35%/a, compounded annually.

c) $25 000 for 8 years at 4.5%/a, compounded quarterly.

d) $50 000 for 4 years at 4.25%/a, compounded monthly.

e) $44 000 for 6 ½ years at 5.5%/a, compounded semi-annually.

Solutions:

 

 
                         

 

 

 

 

 
 


 

 

 

 
 


                                                                                                                                                                                                                                                                                                                                                                       

 

                       

2.  Calculate the amount for each term deposit and the interest paid at the end of the term.

a) $17 000 for 3 years at 4.4%/a, compounded quarterly.

b) $7500 for 5 years at 4%/a, compounded semi-annually.

c) $ 24 000 for 6 years at 5.5%/a, compounded monthly.

d) $ 14 000 for 7 years at 4.4%/a, compounded daily.

Solutions:

 

 

 

 

 

 

 

 

 

 

 

 
 


 

 

 

 
 


 

 

 

3.  On the birth of their grandson, Carole and John invested $5000 for his education.  If the investment pays 8%/a, compounded monthly, how much will be available for his education when he turns 18?

Solution:

 

 

 

 

 

4.  Barry wins $250 000 in the lottery.  If he invest $200 000 of it for 3 years at 6%/a, compounded quarterly, how much interest will he have earned?

   

Solution:

 

 

 

 

5.  Nancy invested $2000 from his summer job in a Guaranteed Investment Certificate (GIC).  He is saving to go to university in 3 years.  How much will he have if interest is 6.54%/a, compounded monthly?

Solution:

 

 

 

6.  The population of Cardiff is now 125 000.  If it grows at a rate of 1.5%/a, what will it’s population be in 25 years?

 

Solution:

 

 

7.  If Ontario’s energy consumption is 1650 megawatts in the year 2000 and is projected to grow at a rate of 5%/a, what will the consumption be

in year 2050 ?

Solution:

 

 

8.  Raja won $100 000 in the lottery.  He invested half of it in a GIC which pays 5.6%/a, compounded quarterly and the rest in a bond that pays 4.8%/a compounded semi-annually.  How much will he have in 10 years?

 
Solution:

 

 

9.  Compare the following investments.  Which is better?

a)  $20 000 invested for 6 years at 5%/a, compounded semi-annually.

Solution:

 

 

 

 

 

 

 
b)  $20 000 invested for 6 years at 5%/a, compounded monthly.

Solution:

 

 

 

 

 

c)  $20 000 invested for 6 years at 5%/a, compounded daily.

Solution:

 

 

Hence you earn more money the more frequently interest is compounded.

The  compounded daily option is the best.

 

 

 

 

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