working in the financial world: compound and simple interest

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WORKING WITH INTEREST
X-Kit Textbook
Chapter 4
CONTENT
Simple
Interest
Compound
Interest
Time Lines
TERMINOLOGY
Term Explanation
Investment When you save money
Loan When you borrow money
Debt When you owe money
Interest • The price you pay for borrowing
money.
• Earning for saving money.
• Interest is added to the original
loan or investment.
SIMPLEINTEREST
Jim wants to study graphic design at
a college and needs R10 000 for his
studies. He goes to a bank to
borrow the money. The bank ask 5%
interest on study loans. At the bank
the following is discussed:
TERMINOLOGY
Term Explanation
Present Value (PV) • The amount of money we borrow or save
• The value today/now
• The principal part of the loan
• Amount before adding interest
• Example R10 000
Interest Rate (𝒊) • The rate is used to calculate the amount of
interest
• Given as percentages
• Change to decimal fractions
• Example 𝟓% = 𝟎, 𝟎𝟓
Interest (I) • The amount we pay (borrow) or get (save)
TERMINOLOGY
Term Explanation
Term of period (𝒏) • The length of time over which we borrow or
save money
• Due date for paying back the a loan
• Maturity date for an investment
• Measure term in years, half-years, months,
weeks or days
• The longer the term, the greater the
amount of interest
Future Value (FV) • The value of money at the end of the term
• The sum of the principal and interest

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𝑰 = 𝑷𝑽 × 𝒊 × 𝒏
• Simple interest is interest that is calculated on the
principal amount for the length of time for which it is
borrowed.
• Simple interest is due at the end of the term
• We calculate simple interest by multiplying the present
value by the interest rate by the term
• Always use the same length of time to measure the rate of
interest and the term, for example:
If the interest rate is per year and the term is for 8 months,
show the term as a fraction of a year ( 𝟖
𝟏𝟐)
Example
Calculate the simple interest that Jim has to pay the
bank if he borrows R10 000 for 1 year. The interest rate
is 5% per annum.
𝑰 = 𝑷𝑽 × 𝒊 × 𝒏
• 𝐼 = the interest (in rands)
• 𝑃𝑉= the present value (the amount borrowed/saved)
• 𝑖 = rate of interest (a percentage)
• 𝑛 = the term or time
Example
What if Jim borrows the money
for 2 years?
CALCULATINGFUTUREVALUE(FV)
Future Value = Present Value + Interest
𝑭𝑽 = 𝑷𝑽 + 𝑰
𝑭𝑽 = 𝑷𝑽 + 𝑷𝑽 × 𝒊 × 𝒏
𝑭𝑽 = 𝑷𝑽 𝟏 + 𝒊𝒏
Example
Jim wants to know how much
he will have to pay in interest on
a 3-year loan of R10 000. Jim
also wants to know how much
money he will have paid in total
by the end of the loan period?
CALCULATINGPRESENTVALUE(PV)
𝑭𝑽 = 𝑷𝑽 𝟏 + 𝒊𝒏
𝑷𝑽 =
𝑭𝑽
𝟏 + 𝒊𝒏

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Example
Jim is still at school and can make
some money as a waiter during the
holidays. Instead of borrowing the
money, Jim wants to save for his
studies. He wants to know how much
money he must save now, at 5%
simple interest to have R10 000 in 3
years’ time?
CALCULATINGINTERESTRATE (𝒊)
𝑭𝑽 = 𝑷𝑽 𝟏 + 𝒊𝒏
Jim made a lot of money in tips working as a
waiter over the summer holidays. He wants to
put R8 500 in the bank to save for his post-
matric studies. He has calculated the future
value. He will need R10 000 for his studies in 3
years’ time. How much interest will he have to
earn on his principal of R8 500? What is the
required interest rate?
CALCULATINGTHE TERM(𝒏)
𝑭𝑽 = 𝑷𝑽 𝟏 + 𝒊𝒏
Jim has R8 000 and he can bank it at an
interest rate of 5%. He still thinks that he
would need R10 000 for his studies. Jim
wants to know how long it will take the
present value of R8 000 to grow to a future
value of R10 000 at a simple interest rate
of 5%?
CALCULATINGSIMPLEINTERESTFOR A
FRACTIONOF THETERM
Jim invested R8 000 for 7 months before he
plans to begin college. What interest will Jim
receive if he banks R8 000 for 7 months at
4.5% simple interest per annum?
You are asked to calculate interest (amount in
rands), not interest rate (a percentage)
Example
Grace receives R750 on her birthday. She
decides to invest the money for 8 months
at 6% per annum.
1. Find the simple interest.
2. Find the future value.
Example
To have a future value of R1 050 after 7
months, how much money must Jim save
at 8% simple interest per annum?
(Remember to change the time to the
same unit as the interest rate.)

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Example
Mary banked R500. After 180 days the
amount in her account is R507. What was
the interest rate that she received?
Example
Joe banked R500 at a bank that gave him
3% interest per annum. When he looked
at his balance (the amount in the bank) it
was R520. How long had Joe’s money
been in the bank?
TIMELINES
Beginning
of Term
Time
Period
Interest
Rate
End of
Term
Example
When Jim started high school, Jim’s mother
began to save for his post-matric studies. She
calculated that 5 years from then, when Jim
leaves school, he will need at least R20 000 to
study for 2 years. Jim’s mother has a savings
account at a bank that pays 4,5% interest per
year. How much would she have to save today
in order to have R20 000 in 5 years’ time? Show
your calculations on a time line.
Example
A man is offered R200 000 cash now for his
house or R202 000 after 6 months. Which
is the better offer if the current interest
rate is 5% per year? Present all
information on a time line.
COMPOUNDINTEREST–
Interestupon Interest
•Compound interest is interest paid on the
original investment as well as on the
interest that you have earned previously.
•Simple interest is only earned on the
original principal.

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R100investedat 10% annually
Year Simple Interest Compound Interest
1 R100 + R10 = R110 R100 + R10 = R110
2 R110 + R10 = R120 R110 + R11 = R121
3 R120 + R10 = R130 R121 + R12,10 = R133,10
4 R130 + R10 = R140 R133,10 + R13,31 = R146,41
5 R140 + R10 = R150 R146,41 + R14,64 = R161,05
10 R190 + R10 = R200 R235,79 + R23,58 = R259,37
50 R590 + R10 = R600 R10 671,90 + R1 067,19 = R11 739,09
WORKINGWITH COMPOUNDINTEREST
𝑭𝑽 = 𝑷𝑽 𝟏 + 𝒊 𝒏
• 𝐹𝑉 = Future Value
• 𝑃𝑉 = Present Value (Principal)
• 𝑖 = Annual Interest Rate
• 𝑛 = Number of years/period
•We can change the subject of the formula
CALCULATINGFUTUREVALUE
Jim receives R1 000 on his birthday and
decides to save it. He can get an interest
rate of 4% at the bank. Interest is
compounded annually (yearly). Jim wants
to know how much his investment will be
worth at the end of 3 years.
EXAMPLE
In 10 years’ time, you want to have your
own business. You believe that it is better
to start small than not to start saving at all.
You invest R5 000 now and leave it for 10
years. Interest is compounded at 8%
annually.
CALCULATINGPRESENTVALUE
Before you start your own business, you’d
like to travel. In 7 years’ time, you think
you would need at least R85 000 to see
some of the world. How much money
would you need to invest now? The
interest rate is 18% p.a. compounded
annually.
CALCULATINGINTERESTRATE
A friend wants to borrow R3 000 from you.
She says that she will give you R4 000 back
after 3 years. But, you know about compound
interest. You know that if you put your R3 000
in a bank for 3 years, you will earn compound
interest at a rate of 8% p.a. What is the
interest rate if you lend your friend the
money?

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CALCULATINGTHE TERM/PERIOD
Your younger brother earns R500 working
in your family’s shop during the school
holidays. He wants to buy a bicycle so that
he can make more money by delivering
pizzas. His dream bicycle cost R700. How
long will he have to save if he can earn 8%
interest compounded annually?
DIFFERENTTIMEPERIODS
• Interest compounded annually means that the interest is added
to the capital amount ones a year at the end of the year.
• To handle different time periods the compound interest
formula is changed:
𝑭𝑽 = 𝑷𝑽 𝟏 +
𝒊
𝒎
𝒏×𝒎
• 𝐹𝑉 = Future Value after 𝑛 × 𝑚 periods of compounding
• 𝑃𝑉 = Present Value
• 𝑖 = Compound Interest Rate
• 𝑚 = Number of compounding periods during one year
• 𝑛 = Number of years that the investment is held
EXAMPLE
Let’s see how much R1 000 would be
worth if we invested it for 10 years at 5%
interest, and interest is compounded:
1. Annually
2. Semi-annually
3. Quarterly
4. Monthly
5. Daily
The Future Value increases as
the compounding periods
increase.
MORE EXAMPLES
Find the future value of R200 invested for 7
years at 7,5% per annum and compounded
annually.
MORE EXAMPLES
You have won a scratch-and-win
competition held by your bank. You can
choose one of the following prizes:
•R10 000 now, or
•R18 000 at the end of 5 years
The interest rate is 12% compounded
annually. Which prize do you choose?

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MORE EXAMPLES
For R2 000 to become R3 000 in 10 years,
work out what the annual compound
interest rate should be.
MORE EXAMPLES
How long will it take R2 000 to grow
to R3 000 at 8% interest compounded
annually?
MORE EXAMPLES
Jim saves R500 at an interest rate of 6%.
What is his investment worth after 5 years
if interest is compounded:
1. Yearly
2. Quarterly
3. Monthly
4. Weekly
5. Daily