1. Finance and Growth
By: Georgina Fourie
Student Number: 201223436
Module Code: PFS3A10
Date: 09 March 2014

2. Content
Interest and Interest Rates
 The difference between interest and interest rates.
 Terminology.
 Simple Interest.
 Compound Interest.
Foreign Exchange Rates
 Current exchange rates.
 Writing exchange rates as ratios.

3. The Difference Between
Interest and Interest Rates
Interest : This is seen as money in the context of
finance and can be seen as two things
Interest earned – The reward that a bank or
company will pay their clients for depositing or
investing money with them.
2. Interest owed – The fee or charge that a person
pays for borrowing money
1.

4. The Difference Between
Interest and Interest Rates

Interest Rate – This is the rate at which a person
is rewarded for money that has been invested or
charged for money that has been borrowed.
Interest rate is usually
expressed as a
percentage

5. The Difference Between
Interest and Interest Rates
Example:
Nomsa takes R18 000 student loan from the bank to
pay for her studies. The bank is charging her 12%
interest per annum on the loan.


This rate of 12% is the INTEREST RATE.
The amount Nomsa has to pay back to the bank
every month is the INTEREST.

6. Terminology

Hire purchase loan repayments are calculated
using simple interest formula on cash price, less
deposit.

Monthly repayments are calculated by dividing
the accumulated amount by the number of months
for the repayment.

7. Terminology

Inflation is the average increase in the price of
goods each year and is given as a percentage.

Population growth is calculated using compound
interest formula.

Foreign exchange rate is the price of one
currency in terms of another.

8. Simple Interest

Simple interest is interest that is calculated on the
principal or original amount for the length of time
for which it is borrowed. Simple interest is due at
the end of the term.
Another word for simple
interest is Hire Purchase

9. Simple Interest
Formula:
A = P(1+n×i)
A  Final amount.
 P  Initial/Principle amount.
 n  Number of increases/decreases.
 i  Rate of interest per increase/decrease.


10. Simple Interest
Example:
Find the final amount if R860 is invested for 3 years
at 5% simple interest?

11. Simple Interest
Solution:
A=? , P=R860 , n=3 years , i=5%
A=P(1+n×i)
A= 860 (1+3×0.05)
A=R989,00c

12. Simple Interest
Manipulating the formula to find i
Original formula : A = P(1+n×i)
Manipulated formula:

13. Simple Interest

For Example:
An investment of R500 increases to R1243 after 2
years. Determine the rate at which simple interest
is being calculated on the investment.

14. Simple Interest
A = R1243, i = ?, n = 2 years, P = R500

15. Compound Interest

Compound interest is called ‘interest upon interest’
because it is interest that is being paid on the
original investment as well as on the interest that
you have earned previously.
Another word for
compound interest is
Inflation.

16. Compound Interest
Formula:
A= P(1+i)ⁿ
A  Final amount.
 P  Initial/Principle amount.
 n  Number of increases/decreases.
 i  Rate of interest per increase/decrease.


17. Compound Interest
Compound interest can be calculated:






Annually – Keep original numbers.
Half-yearly – i = ÷2 ; n = ×2
Quarterly – i = ÷4 ; n = ×4
Monthly - i = ÷12 ; n = ×12
Weekly - i = ÷52 ; n = ×52
Daily – i = ÷365 ; n = ×365

18. Compound Interest
Example:
Jim receives R1000 on his birthday and decides to
save it. He can get an interest rate of 4% at the
bank. Interest is compounded annually for 3 years.
How much will Jims investment be worth after the 3
years?

19. Compound Interest
Solution:
A=? , P=R1000 , n=3 years , i=4%
A= P(1+i)ⁿ
A= 1000(1+ 0.04)³
A= R1124.86c

20. Complex Example
Question:
1. Michael invests R3500 in a savings account. The
interest rate for the first 4 years is 8% p.a.
compounded monthly, thereafter the interest rate is
changed to 9% p.a. compounded half-yearly for the
next 5 years. Determine the amount of money that
Michael had in his savings account at the end of
this period.

21. Complex Example
Solution:
Part A:
A=? , P=R3500 , n=4×12 , i=8%÷12
A= P(1+i)ⁿ
A= 3500(1+ 0.08÷12)
A= R4814.83c

22. Complex Example
Solution:
Part B:
A=? , P=R4814.83 , n=5×2 , i=9%÷2
A= P(1+i)ⁿ
A= 4814.83(1+ 0.09÷2)
A= R7477.29c
Therefore Michael had R7477.29c in his savings
account

23. Compound Interest
Manipulating the formula to get i
Original formula: A= P(1+i)ⁿ
Manipulated formula:

24. Compound Interest
For Example:
Mpho invests R 30 000 into an account that and after
investing for 4 years compound interest he had
R40 146,76c. What was his interest rate if it was
compounded annually .
Use the formula:

25. Compound Interest
A = R40 146,76, P= R30 000, i = ?, n = 4

26. Exchange Rates
Exchange rates refer to the
cost of buying currencies
from different countries.
A ‘currency’ is the type of
money that a country uses
to buy and sell goods and
services

27. Current Exchange Rates
The table below shows the exchange rates of various
currencies and what they buy and sell each
currency for at this present time.

28. Writing Exchange Rates
as Ratios

An exchange rate is a ratio that shows the price of
one currency in terms of another currency
For example:
Write the following in its simplest ratio if the
exchange rate of R6,9363 is equal to $1.00.
R6,9363: $1.00

29. Writing Exchange Rates as
Ratios
Another Example:
Write the following in its simplest ratio if the exchange
rate of R6,9363 is equal to $1.00, how many
dollars are you able to receive if you have R200.

30. Reference List

Siyavula (2012). Finance Grade 10. Available
From:
http://www.slideshare.net/Siyavula_Education/finan
ce-and-growth?qid=9cccb4a8-91ad-4ec6-b34dbb54860c4721&v=qf1&b=&from_search=2
(Accessed on 07th March 2014).

Mfuphi, M.(2012). Financial Mathematics. Available
From:
http://www.slideshare.net/201035224/financialmathematics?qid=3c4ede27-eafb-48aa-ad8db3ff8a7602bc&v=qf1&b=&from_search (Accessed
on 07th March 2014).

31. Reference List
Xehgo, V. (2014). Financial Mathematics Simple
and Compound Interest. Available From:
http://www.slideshare.net/Vukile/201218457financial-mathematics?qid=3b8ec53b-8b90-47db9ef6-1f4b7ec96a87&v=default&b=&from_search=4
( Accessed on 08th March 2014).
 Mbhamali, T.(2014). Mathematics for grade 10-12.
Available From:
http://www.slideshare.net/Mbhamalitn/financialmathematics-for-grade-10-11-and12?qid=3b8ec53b-8b90-47db-9ef61f4b7ec96a87&v=default&b=&from_search=7
(Accessed on 08th March 2014).


32. Reference List


Nsimbini, N.(2013). Financial Mathematics Mixed
Problems. Available From:
http://www.slideshare.net/Nelisiwepeace/financialmathematics-mixed-problems?qid=3b8ec53b8b90-47db-9ef61f4b7ec96a87&v=default&b=&from_search=5
(Accessed on 09th March 2014).
Kmwangi, (2009). Financial Mathematics. Available
From: http://www.slideshare.net/kmwangi/powmathematician-on-wall-street?qid=23c08bed-890f474f-8b2ad8cfeef02498&v=qf1&b=&from_search=8
(Accessed on 09th March 2014).