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Other applications of compound growth

South Africa's population is increasing by 2,5% per year. If the current population is 43 million, how many more people will there be in South Africa in two years' time ?

    • initial value (opening balance), P = 43 000 000
    • period of time, n = 2 year
    • rate of increase, i = 2 , 5 % per year

    We are required to find the closing balance( A ).

  1. We know from [link] that:

    A = P ( 1 + i ) n
  2. A = P ( 1 + i ) n = 43 000 000 ( 1 + 0 , 025 ) 2 = 45 176 875
  3. There will be 45 176 875 - 43 000 000 = 2 176 875 more people in 2 years' time

A swimming pool is being treated for a build-up of algae. Initially, 50 m 2 of the pool is covered by algae. With each day of treatment, the algae reduces by 5%. What area is covered by algae after 30 days of treatment ?

    • opening balance, P = 50 m 2
    • period of time, n = 30 days
    • rate of increase, i = 5 % per day

    We are required to find the closing balance( A ).

  1. We know from [link] that:

    A = P ( 1 + i ) n

    But this is compound decrease so we can use the formula:

    A = P ( 1 - i ) n
  2. A = P ( 1 - i ) n = 50 ( 1 - 0 , 05 ) 30 = 10 , 73 m 2
  3. Therefore the area still covered with algae is 10 , 73 m 2

Compound interest

  1. An amount of R3 500 is invested in a savings account which pays compound interest at a rate of 7,5% per annum. Calculate the balance accumulated by the end of 2 years.
  2. If the average rate of inflation for the past few years was 7,3% and your water and electricity account is R 1 425 on average, what would you expect to pay in 6 years time ?
  3. Shrek wants to invest some money at 11% per annum compound interest. How much money (to the nearest rand) should he invest if he wants to reach a sum of R 100 000 in five year's time ?


  • A foreign exchange rate is the price of one currency in terms of another.
  • There are two types of interest: simple and compound.
  • The following table summarises the key definitions that are used in both simple and compound interest.
    P Principal (the amount of money at the starting point of the calculation)
    A Closing balance (the amount of money at the ending point of the calculation)
    i interest rate, normally the effective rate per annum
    n period for which the investment is made
  • For simple interest we use:
    A = P ( 1 + i · n )
  • For compound interest we use:
    A = P ( 1 + i ) n
Always keep the interest and the time period in the same units of time (e.g. both in years, or both in months etc.).

The following three videos provide a summary of how to calculate interest. Take note that although the examples are done using dollars, we can use the fact that dollars are a decimal currency and so are interchangeable (ignoring the exchange rate) with rands. This is what is done in the subtitles.

Khan academy video on interest - 1

Khan academy video on interest - 2

Note in this video that at the very end the rule of 72 is mentioned. You will not be using this rule, but will rather be using trial and error to solve the problem posed.

Khan academy video on interest - 3

End of chapter exercises

  1. You are going on holiday to Europe. Your hotel will cost 200 euros per night. How much will you need in Rands to cover your hotel bill, if the exchange rate is 1 euro = R9,20?
  2. Calculate how much you will earn if you invested R500 for 1 year at the following interest rates:
    1. 6,85% simple interest.
    2. 4,00% compound interest.
  3. Bianca has R1 450 to invest for 3 years. Bank A offers a savings account which pays simple interest at a rate of 11% per annum, whereas Bank B offers a savings account paying compound interest at a rate of 10,5% per annum. Which account would leave Bianca with the highest accumulated balance at the end of the 3 year period?
  4. How much simple interest is payable on a loan of R2 000 for a year, if the interest rate is 10%?
  5. How much compound interest is payable on a loan of R2 000 for a year, if the interest rate is 10%?
  6. Discuss:
    1. Which type of interest would you like to use if you are the borrower?
    2. Which type of interest would you like to use if you were the banker?
  7. Calculate the compound interest for the following problems.
    1. A R2 000 loan for 2 years at 5%.
    2. A R1 500 investment for 3 years at 6%.
    3. An R800 loan for l year at 16%.
  8. If the exchange rate for 100 Yen = R 6,2287 and 1 Australian Doller (AUD) = R 5,1094 , determine the exchange rate between the Australian Dollar and the Japanese Yen.
  9. Bonnie bought a stove for R 3 750. After 3 years she had finished paying for it and the R 956,25 interest that was charged for hire-purchase. Determine the rate of simple interest that was charged.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [ncs]. OpenStax CNX. Aug 05, 2011 Download for free at http://cnx.org/content/col11239/1.2
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