201201797 TN MBHAMALI

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201201797•Mr TN MBHAMALI

•MATHEMATICS FOR GRADE 10-12

09/05/2013

Financial Mathematics FOR

Grade 10 – 12

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Learning Style• allocate sufficient study time• briefly revise the prerequisite material• attempt every guided exercise and most of the

other exercises

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Content• Content

Simple Interest

Compound Interest

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Working with Simple Interest

• Formulae

• 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:

Given: If the interest rate is per year and the term is for 8 months, show the term as a fraction of a year ( ) 𝟖𝟏𝟐

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Example: Working with Simple Interest

• Calculate the simple interest that Jimmy has to pay the bank if he borrows R10 000 for 1 year. The interest rate is 5% per annum.

-Data.• the interest (in rands)• the present value (the amount borrowed/saved)• rate of interest (a percentage)• the term or time

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CALCULATING FUTURE VALUE (FV) • Future Value = Present Value + Interest

=

• Example:Jimmy wants to know how much he will have to pay in interest on a 3-year loan of R10 000. Jimmy also wants to know how much money he will have paid in total by the end of the loan period?Data

= =

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CALCULATING PRESENT VALUE (PV)

• ExampleJimmy 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?-DATA

= = =

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CALCULATING Interest Rate (𝑖)

• Example: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?Data

•

= = = =

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CALCULATING THE TERM ( )𝒏• ExampleJimmy 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%?DATA

= =

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WORKING WITH COMPOUND

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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R100 invested at 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

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WORKING WITH COMPOUND

INTEREST• Formulae • Future Value• Present Value (Principal)

• Number of years/period• Annual Interest Rate

• We can change the subject of the formula as we have done from Simple interest Formulae

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CALCULATING FUTURE VALUE

• ExampleJimmy 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.Data

= =

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CALCULATING PRESENT VALUE

• ExampleBefore 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.DATA

= = =

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CALCULATING Interest Rate (𝑖)

• ExampleA 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?

Data

= = = = = =

=

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CALCULATING THE TERM ( )𝒏• ExampleYour 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?

Data

• ?? = = = = =

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The end OF the slides for Today!!!!!!!

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THANK YOU!!!

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