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 chaPTer 11 FINANCE AND GROWTH 349
11 
Finance and growth
This chapter focuses on the spending and investing value  
of money.
In this chapter, you will learn:
•	 how to calculate simple interest
•	 how to calculate compound interest
•	 how to compare different investments
•	 about hire purchase
•	 about inflation and its effects
•	 about exchange rates and their effects
2153 TechMaths Eng G10 LB.indb   349 2015/10/22   3:41 PM
Page 2


 chaPTer 11 FINANCE AND GROWTH 349
11 
Finance and growth
This chapter focuses on the spending and investing value  
of money.
In this chapter, you will learn:
•	 how to calculate simple interest
•	 how to calculate compound interest
•	 how to compare different investments
•	 about hire purchase
•	 about inflation and its effects
•	 about exchange rates and their effects
2153 TechMaths Eng G10 LB.indb   349 2015/10/22   3:41 PM
350 Technical Ma TheMaTicS Grade 10
11.1 investing through simple interest
Situation: Mimi’s friend, Modiba, an experienced builder, wants to start his own construction 
company. He has a bit of savings but needs extra money to buy equipment.
He asks Mimi to invest R12 500 in his business. He promises to pay her back when his business 
is up and running. After doing a few calculations, they draw up an agreement for how he will 
repay her. They agree that he will also pay her 1,75% interest of the investment amount for 
each month, until he repays her. When he repays her, he will owe her the R12 500 plus the total 
interest up to the end of the current month. Mimi trusts Modiba completely and knows he will 
repay her everything when he has the money.
From Mimi’s point of view, she is investing R12 500 in Modiba’s start-up business. She 
represents the situation for herself on a timeline – a number line for time:
owed to me 
after month n
R12 500 +  
n(1,75% of R12 500)
R12 500 +  
3 × n(1,75% of R12 500)
R12 500 +  
2 × n(1,75% of R12 500)
R12 500 +  
1 × n(1,75% of R12 500)
R12 500
owed to me 
after month 3
owed to me 
after month 2
owed to me 
after month 1
principal 
amount owed 
to me
Final value of Mimi’s investment = R 12 500 + total interest
 = R12 500 + R12 500 ×   
1,75
 
_____
 
100
   × number of months
 = R12 500 ×  
(
? 1 +   
1,75
 
_____
 
100
   × number of months 
)
 
Let us use some symbols for the different quantities in our example: 
A final total value of the investment (called the accumulated value)
P initial amount invested (called the principal value)
i interest rate per time unit, here per month, expressed as a decimal fraction
n number of time units, here number of months, over which interest is    
calculated
2153 TechMaths Eng G10 LB.indb   350 2015/10/22   3:41 PM
Page 3


 chaPTer 11 FINANCE AND GROWTH 349
11 
Finance and growth
This chapter focuses on the spending and investing value  
of money.
In this chapter, you will learn:
•	 how to calculate simple interest
•	 how to calculate compound interest
•	 how to compare different investments
•	 about hire purchase
•	 about inflation and its effects
•	 about exchange rates and their effects
2153 TechMaths Eng G10 LB.indb   349 2015/10/22   3:41 PM
350 Technical Ma TheMaTicS Grade 10
11.1 investing through simple interest
Situation: Mimi’s friend, Modiba, an experienced builder, wants to start his own construction 
company. He has a bit of savings but needs extra money to buy equipment.
He asks Mimi to invest R12 500 in his business. He promises to pay her back when his business 
is up and running. After doing a few calculations, they draw up an agreement for how he will 
repay her. They agree that he will also pay her 1,75% interest of the investment amount for 
each month, until he repays her. When he repays her, he will owe her the R12 500 plus the total 
interest up to the end of the current month. Mimi trusts Modiba completely and knows he will 
repay her everything when he has the money.
From Mimi’s point of view, she is investing R12 500 in Modiba’s start-up business. She 
represents the situation for herself on a timeline – a number line for time:
owed to me 
after month n
R12 500 +  
n(1,75% of R12 500)
R12 500 +  
3 × n(1,75% of R12 500)
R12 500 +  
2 × n(1,75% of R12 500)
R12 500 +  
1 × n(1,75% of R12 500)
R12 500
owed to me 
after month 3
owed to me 
after month 2
owed to me 
after month 1
principal 
amount owed 
to me
Final value of Mimi’s investment = R 12 500 + total interest
 = R12 500 + R12 500 ×   
1,75
 
_____
 
100
   × number of months
 = R12 500 ×  
(
? 1 +   
1,75
 
_____
 
100
   × number of months 
)
 
Let us use some symbols for the different quantities in our example: 
A final total value of the investment (called the accumulated value)
P initial amount invested (called the principal value)
i interest rate per time unit, here per month, expressed as a decimal fraction
n number of time units, here number of months, over which interest is    
calculated
2153 TechMaths Eng G10 LB.indb   350 2015/10/22   3:41 PM
 chaPTer 11 FINANCE AND GROWTH 351
This leads us to a formula and proper definition of simple interest:
simple interest is calculated only on the principal value: 
A = P (1 + in)
The total interest is given by A - P = Pin
Where is simple interest used? Usually in situations where it is important to keep things easy  
to understand:
•	 Informally, for private loans between individuals; financial institutions such as banks usually 
use compound interest – see the next section.
•	 Grassroots community banking, where loans are made simple to understand.
•	 Government bonds, which are really just loans to the government by individuals; the 
government guarantees that it will pay interest on certain fixed dates.
•	 Hire purchase.
•	 In situations where interest is paid out during the time, and not at the end e.g. if Modiba paid 
Mimi the interest every month, instead of at the end.
exercises
1  Mimi pays the R12 500 into Modiba’s business account on 1 March 2015.
 Mimi draws up the following table for Modiba, showing how much he owes each month for 
the first year:
if you pay  
back on
n, number of 
months you take  
to repay me
A - P, the total interest 
you owe me (to the 
nearest cent)
A, the total amount you 
owe me (to the nearest 
cent)
1 March 2015 0 R0 R12 500
1 April 2015 1
1 May 2015 2
1 June 2015 3
1 July 2015 4 R875 R13 375
1 August 2015 5
1 September 2015 6
1 October 2015 7
1 November 2015 8
1 December 2015 9
1 January 2016 10 R2 187,50 R14 687,50
1 February 2016 11
1 March 2016 12
2153 TechMaths Eng G10 LB.indb   351 2015/10/22   3:41 PM
Page 4


 chaPTer 11 FINANCE AND GROWTH 349
11 
Finance and growth
This chapter focuses on the spending and investing value  
of money.
In this chapter, you will learn:
•	 how to calculate simple interest
•	 how to calculate compound interest
•	 how to compare different investments
•	 about hire purchase
•	 about inflation and its effects
•	 about exchange rates and their effects
2153 TechMaths Eng G10 LB.indb   349 2015/10/22   3:41 PM
350 Technical Ma TheMaTicS Grade 10
11.1 investing through simple interest
Situation: Mimi’s friend, Modiba, an experienced builder, wants to start his own construction 
company. He has a bit of savings but needs extra money to buy equipment.
He asks Mimi to invest R12 500 in his business. He promises to pay her back when his business 
is up and running. After doing a few calculations, they draw up an agreement for how he will 
repay her. They agree that he will also pay her 1,75% interest of the investment amount for 
each month, until he repays her. When he repays her, he will owe her the R12 500 plus the total 
interest up to the end of the current month. Mimi trusts Modiba completely and knows he will 
repay her everything when he has the money.
From Mimi’s point of view, she is investing R12 500 in Modiba’s start-up business. She 
represents the situation for herself on a timeline – a number line for time:
owed to me 
after month n
R12 500 +  
n(1,75% of R12 500)
R12 500 +  
3 × n(1,75% of R12 500)
R12 500 +  
2 × n(1,75% of R12 500)
R12 500 +  
1 × n(1,75% of R12 500)
R12 500
owed to me 
after month 3
owed to me 
after month 2
owed to me 
after month 1
principal 
amount owed 
to me
Final value of Mimi’s investment = R 12 500 + total interest
 = R12 500 + R12 500 ×   
1,75
 
_____
 
100
   × number of months
 = R12 500 ×  
(
? 1 +   
1,75
 
_____
 
100
   × number of months 
)
 
Let us use some symbols for the different quantities in our example: 
A final total value of the investment (called the accumulated value)
P initial amount invested (called the principal value)
i interest rate per time unit, here per month, expressed as a decimal fraction
n number of time units, here number of months, over which interest is    
calculated
2153 TechMaths Eng G10 LB.indb   350 2015/10/22   3:41 PM
 chaPTer 11 FINANCE AND GROWTH 351
This leads us to a formula and proper definition of simple interest:
simple interest is calculated only on the principal value: 
A = P (1 + in)
The total interest is given by A - P = Pin
Where is simple interest used? Usually in situations where it is important to keep things easy  
to understand:
•	 Informally, for private loans between individuals; financial institutions such as banks usually 
use compound interest – see the next section.
•	 Grassroots community banking, where loans are made simple to understand.
•	 Government bonds, which are really just loans to the government by individuals; the 
government guarantees that it will pay interest on certain fixed dates.
•	 Hire purchase.
•	 In situations where interest is paid out during the time, and not at the end e.g. if Modiba paid 
Mimi the interest every month, instead of at the end.
exercises
1  Mimi pays the R12 500 into Modiba’s business account on 1 March 2015.
 Mimi draws up the following table for Modiba, showing how much he owes each month for 
the first year:
if you pay  
back on
n, number of 
months you take  
to repay me
A - P, the total interest 
you owe me (to the 
nearest cent)
A, the total amount you 
owe me (to the nearest 
cent)
1 March 2015 0 R0 R12 500
1 April 2015 1
1 May 2015 2
1 June 2015 3
1 July 2015 4 R875 R13 375
1 August 2015 5
1 September 2015 6
1 October 2015 7
1 November 2015 8
1 December 2015 9
1 January 2016 10 R2 187,50 R14 687,50
1 February 2016 11
1 March 2016 12
2153 TechMaths Eng G10 LB.indb   351 2015/10/22   3:41 PM
352 Technical Ma TheMaTicS Grade 10
 Redraw the table in your exercise book and calculate the missing values. A few values have 
been given so that you can check that you understand the calculations.
(a) Describe in your own words how the amount Modiba owes Mimi changes from month 
to month. Write down an expression that gives the change, using the symbols P and i.
(b) What is the total, i.e. effective, interest rate Modiba pays after three months? After six 
months? After one year? Give your answers as percentages.
 Hint: Calculate the percent increase of the accumulated value compared to the 
principal for each of these three times.
(c) You will need some graph paper for this question. Use your completed table to plot the 
total amount Modiba owes each month, as a graph. The horizontal axis is a time line 
marked in months. The vertical axis is in Rand. What kind of graph do you get? Should 
you ‘connect the dots’ or just leave them as points?
(d) Look carefully at the formula for simple interest. Rewrite the formula in the standard 
form for a straight line function. Clearly indicate where the gradient and where the 
A-intercept are.
(e) The first row for March may seem a little strange because Mimi expects the total interest 
for each month. Does it make mathematical sense though? How?
2  (a)  Redraw the following table and complete the number pattern. The pattern gives the 
multiplication factor for each month that Modiba owes Mimi:
number of months 
until Modiba pays 
Mimi
1 2 3 4 5 … n
Multiplication 
factor in algebraic 
form
1 +   
1,75
 
_____
 
100
  1 + 4 ×   
1,75
 
_____
 
100
  …
Multiplication 
factor in decimal 
form
1,017 5 1,052 5 …
(b)  Go back to exercise 1 (c). Do you notice anything new from before? If you do, describe 
what you notice.
If you understand how the multiplication factor works, the formula for simple interest no 
longer has any secrets to keep from you! 
2153 TechMaths Eng G10 LB.indb   352 2015/10/22   3:41 PM
Page 5


 chaPTer 11 FINANCE AND GROWTH 349
11 
Finance and growth
This chapter focuses on the spending and investing value  
of money.
In this chapter, you will learn:
•	 how to calculate simple interest
•	 how to calculate compound interest
•	 how to compare different investments
•	 about hire purchase
•	 about inflation and its effects
•	 about exchange rates and their effects
2153 TechMaths Eng G10 LB.indb   349 2015/10/22   3:41 PM
350 Technical Ma TheMaTicS Grade 10
11.1 investing through simple interest
Situation: Mimi’s friend, Modiba, an experienced builder, wants to start his own construction 
company. He has a bit of savings but needs extra money to buy equipment.
He asks Mimi to invest R12 500 in his business. He promises to pay her back when his business 
is up and running. After doing a few calculations, they draw up an agreement for how he will 
repay her. They agree that he will also pay her 1,75% interest of the investment amount for 
each month, until he repays her. When he repays her, he will owe her the R12 500 plus the total 
interest up to the end of the current month. Mimi trusts Modiba completely and knows he will 
repay her everything when he has the money.
From Mimi’s point of view, she is investing R12 500 in Modiba’s start-up business. She 
represents the situation for herself on a timeline – a number line for time:
owed to me 
after month n
R12 500 +  
n(1,75% of R12 500)
R12 500 +  
3 × n(1,75% of R12 500)
R12 500 +  
2 × n(1,75% of R12 500)
R12 500 +  
1 × n(1,75% of R12 500)
R12 500
owed to me 
after month 3
owed to me 
after month 2
owed to me 
after month 1
principal 
amount owed 
to me
Final value of Mimi’s investment = R 12 500 + total interest
 = R12 500 + R12 500 ×   
1,75
 
_____
 
100
   × number of months
 = R12 500 ×  
(
? 1 +   
1,75
 
_____
 
100
   × number of months 
)
 
Let us use some symbols for the different quantities in our example: 
A final total value of the investment (called the accumulated value)
P initial amount invested (called the principal value)
i interest rate per time unit, here per month, expressed as a decimal fraction
n number of time units, here number of months, over which interest is    
calculated
2153 TechMaths Eng G10 LB.indb   350 2015/10/22   3:41 PM
 chaPTer 11 FINANCE AND GROWTH 351
This leads us to a formula and proper definition of simple interest:
simple interest is calculated only on the principal value: 
A = P (1 + in)
The total interest is given by A - P = Pin
Where is simple interest used? Usually in situations where it is important to keep things easy  
to understand:
•	 Informally, for private loans between individuals; financial institutions such as banks usually 
use compound interest – see the next section.
•	 Grassroots community banking, where loans are made simple to understand.
•	 Government bonds, which are really just loans to the government by individuals; the 
government guarantees that it will pay interest on certain fixed dates.
•	 Hire purchase.
•	 In situations where interest is paid out during the time, and not at the end e.g. if Modiba paid 
Mimi the interest every month, instead of at the end.
exercises
1  Mimi pays the R12 500 into Modiba’s business account on 1 March 2015.
 Mimi draws up the following table for Modiba, showing how much he owes each month for 
the first year:
if you pay  
back on
n, number of 
months you take  
to repay me
A - P, the total interest 
you owe me (to the 
nearest cent)
A, the total amount you 
owe me (to the nearest 
cent)
1 March 2015 0 R0 R12 500
1 April 2015 1
1 May 2015 2
1 June 2015 3
1 July 2015 4 R875 R13 375
1 August 2015 5
1 September 2015 6
1 October 2015 7
1 November 2015 8
1 December 2015 9
1 January 2016 10 R2 187,50 R14 687,50
1 February 2016 11
1 March 2016 12
2153 TechMaths Eng G10 LB.indb   351 2015/10/22   3:41 PM
352 Technical Ma TheMaTicS Grade 10
 Redraw the table in your exercise book and calculate the missing values. A few values have 
been given so that you can check that you understand the calculations.
(a) Describe in your own words how the amount Modiba owes Mimi changes from month 
to month. Write down an expression that gives the change, using the symbols P and i.
(b) What is the total, i.e. effective, interest rate Modiba pays after three months? After six 
months? After one year? Give your answers as percentages.
 Hint: Calculate the percent increase of the accumulated value compared to the 
principal for each of these three times.
(c) You will need some graph paper for this question. Use your completed table to plot the 
total amount Modiba owes each month, as a graph. The horizontal axis is a time line 
marked in months. The vertical axis is in Rand. What kind of graph do you get? Should 
you ‘connect the dots’ or just leave them as points?
(d) Look carefully at the formula for simple interest. Rewrite the formula in the standard 
form for a straight line function. Clearly indicate where the gradient and where the 
A-intercept are.
(e) The first row for March may seem a little strange because Mimi expects the total interest 
for each month. Does it make mathematical sense though? How?
2  (a)  Redraw the following table and complete the number pattern. The pattern gives the 
multiplication factor for each month that Modiba owes Mimi:
number of months 
until Modiba pays 
Mimi
1 2 3 4 5 … n
Multiplication 
factor in algebraic 
form
1 +   
1,75
 
_____
 
100
  1 + 4 ×   
1,75
 
_____
 
100
  …
Multiplication 
factor in decimal 
form
1,017 5 1,052 5 …
(b)  Go back to exercise 1 (c). Do you notice anything new from before? If you do, describe 
what you notice.
If you understand how the multiplication factor works, the formula for simple interest no 
longer has any secrets to keep from you! 
2153 TechMaths Eng G10 LB.indb   352 2015/10/22   3:41 PM
 chaPTer 11 FINANCE AND GROWTH 353
w orked example 
Problem: A sum of money is invested at 12% p.a. simple interest. After seven years, the value 
of the investment is R23 920. What amount was invested?
Solution:
 A = P(1 + in) A = 23 920
 23 920 = P(1 + 0,12 × 7) i =   
12
 
____
 
100
   = 0, 1 2
 so P =   
23 920
 
____________
  
(1 + 0,12 × 7)
   P = ?
 = R13 000 n = 7
w orked example 
Problem: R6 000 is invested using simple interest calculated every month for 30 months.  
The total interest is R1 125. What is the monthly interest rate as a percent?
Solution 1: Using the formula directly 
 A = P(1 + in) A = 6 000 + 1 125 = 7 125
 7 125 = 6 000(1 + i × 30) P = 6 000
 so 1 + 30i =   
7 125
 
______
 
6 000
   i = ?
 30i =   
7 125
 
______
 
6 000
   - 1 n = 30
 i =   
7 125
 
______
 
  
6 000
 
______
 
30
  
   - 1
 = 6,25 × 1 0 
-3
 
 Therefore, % interest = 100 × i = 0,625% per month
Solution 2: Working smart and using the interest part of the formula.
 1 125 = 6 000 × i × 30 A - P = 1 125
 so i =   
1 125
 
_________
 
6 000 × 30
   P = 6 000
  i = ?
  n = 30
 Therefore, % interest = 0,625% per month
2153 TechMaths Eng G10 LB.indb   353 2015/10/22   3:41 PM
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FAQs on Textbook: Finance and Growth - Mathematics for Grade 10

1. What is the relationship between finance and economic growth?
Ans. Finance plays a crucial role in economic growth by facilitating investments, providing capital for businesses, and enabling individuals to save and invest. Access to adequate financial resources allows for the development of new technologies, expansion of businesses, and creation of jobs, all of which contribute to overall economic growth.
2. How does financial literacy impact growth in a community?
Ans. Financial literacy empowers individuals with the knowledge and skills to make informed decisions about saving, investing, and managing debt. In a community where residents are financially literate, there is likely to be increased savings rates, better investment in education and health, and overall economic stability, which can lead to sustainable growth.
3. What are some common challenges faced in accessing finance for growth?
Ans. Common challenges include high interest rates, lack of collateral, limited access to banking services, and insufficient financial education. These barriers can hinder individuals and small businesses from obtaining the necessary funds to invest in growth opportunities, which can stifle economic development.
4. How can governments promote finance and growth?
Ans. Governments can promote finance and growth by implementing policies that enhance access to financial services, such as supporting microfinance institutions, incentivizing investments in key sectors, and providing financial education programs. Additionally, creating a stable regulatory environment can encourage both domestic and foreign investments.
5. What role do banks play in fostering economic growth?
Ans. Banks play a vital role in economic growth by mobilizing savings and providing loans to individuals and businesses. They assess the creditworthiness of borrowers, allocate resources efficiently, and contribute to the stability of the financial system. By funding projects and innovations, banks help drive economic expansion and job creation.
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