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IB Math Studies – Topic 8

IB Math Studies – Topic 8. Financial Mathematics. IB Course Guide Description. Introduction. Vocabulary : Currency – money Exchange Rate – establishes a relationship between the value of currencies. These are constantly changing. Conversion – exchanging/converting currencies.

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IB Math Studies – Topic 8

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  1. IB Math Studies – Topic 8 Financial Mathematics

  2. IB Course Guide Description

  3. Introduction Vocabulary: • Currency– money • Exchange Rate – establishes a relationship between the value of currencies. These are constantly changing. • Conversion – exchanging/converting currencies. • Commission – amount/percentage made by exchanging agency

  4. Percentage increases and decreases Both: Divide the resulting amount by 100 and multiply by the amount you wish to increase or decrease • To increase a percentage • Add the percentage on to 100 • To decrease a percentage • Take away from 100

  5. Reciprocals • You can use proportions to solve currency conversion questions Example: 1 GBP = 1.80 US $ Cross multiply and divide. x = 0.56 GBP

  6. Commission • Banks and other currency traders earn a commission for exchanging currency. • Commission rates are usually between 0.5% to 3% • If there is no commission, then the exchange rates will be worse

  7. Examples Questions of Commission

  8. Examples Questions of Commission • Converting 500 UK pounds to US dollars were 1 UK pound buys $1.8734 US • Commission: • Customer receives: • Converting 350 UK pounds to euro where 1 UK pound buys $.5071 euro • Commission: • Customer receives: 7.50 pounds $923 US 5.25 pounds 175 euros

  9. Interest • There are two types of interest: simple and compounded. Simple: Compounded:

  10. Simple Interest - Examples • What flat rate of interest does a bank need to charge so that €5000 will earn €900 simple interest in 18 months? • How long will it take $2000 invested at a flat rate of 12.5% p.a. to amount to $3000?

  11. Compound Interest

  12. Compound Interest - Continued

  13. Compound Interest - Examples

  14. Compound Interest - Examples • $5359.57 • $7293.04 • 9300.65 pounds • 113.40 euro • $1170.26 • $6663.24

  15. Repayment • Repayments are often made in regular payments over the length of the loan. • These may be weekly, fortnightly, monthly or another period of time. • Calculate the interest • Calculate the total amount to be repaid (capital + interest) • Calculate the total number of payments • Determine the amount of a regular payment Calculating Repayment

  16. Repayment - Examples

  17. Repayment - Examples • $274.84 • 787.50 baht • $1418.75

  18. Loan and repayment table

  19. Example • Francine takes out a personal loan for $ 16 500 to buy a car. She negotiates a term of 4 years at 11.5% p.a. interest. • Calculate the monthly repayments

  20. Check your answers • From the table, the monthly repayments on each $1000 for 4 years (48 months) at 11.5% p.a. = $26.0890 • Repayments on $16 500 = $26.0890 x 16.5 (16.5 lots of $1000) = $430.4685 = $430.50

  21. Inflation • Inflation is the increase in prices of goods and wages • If inflation rate is constant over a number of years, we can use compounded interest Example: In a period where inflation is running at 5, find the price of a television that originally costs $450 after 4 years. = 450= $546.98

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