IB Math Studies – Topic 8

Financial Mathematics

IB Course Guide Description

IntroductionVocabulary:• 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

Percentage increases and decreases • To increase a percentage– Add the percentage on to 100

• To decrease a percentage – Take away from 100

Both: Divide the resulting

amount by 100 and multiply by the amount you wish to increase or

decrease

Question Working

Increase 200 by 10% 200 + (0.10 x 200) = 200(1 + 0.10) = 200(1.10) = 220

Increase 150 by 15% 150 + (0.15 x 150) = 150(1 + 0.15) = 150(1.15) = 172.5

Increase 300 by 17.5% 300 + (0.175 x 300) = 300(1.175) = 352.5

Decrease 200 by 10% 200 – (0.10 x 200) = 200(1 – 0.10) = 200(0.90) = 180

Decrease 750 by 1.5% 750 – ( 0.015 x 750) = 750 (1 – 0.015) = 750(0.985) = 738.75

Reciprocals • You can use proportions to solve currency

conversion questions Example:

1 GBP = 1.80 US $

Cross multiply and divide. x = 0.56 GBP

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

Examples Questions of Commission

Examples Questions of Commission

1. Converting 500 UK pounds to US dollars were 1 UK pound buys $1.8734 US1. Commission: 2. Customer receives:

2. Converting 350 UK pounds to euro where 1 UK pound buys $.5071 euro1. Commission: 2. Customer receives:

7.50 pounds

$923 US

5.25 pounds

175 euros

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

Simple:

Compounded:

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?

Compound Interest

Compound Interest - Continued

Compounding period

yearly 1 times per year k = 1

half-yearly 2 times per year k = 2

quarterly 4 times per year k = 4

monthly 12 times per year k = 12

daily 365 times per year k = 365

Compound Interest - Examples

Compound Interest - Examples

a) $5359.57b) $7293.04c) 9300.65 pounds

a. 113.40 eurob. $1170.26c. $6663.24

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.

1. Calculate the interest

2. Calculate the total amount to be repaid (capital + interest)

3. Calculate the total number of payments

4. Determine the amount of a regular payment

Calculating Repayment

total to be repaidregular payment =

number of repayments

Repayment - Examples

Repayment - Examples

1. $274.842. 787.50 baht3. $1418.75

Loan and repayment table

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

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

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