IB Math Studies – Topic 8
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.
• 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 $
1 𝐺𝐵𝑃
𝑥 𝐺𝐵𝑃
=
1.80 𝑈𝑆$
1 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 US
1. Commission: 7.50 pounds
2. Customer receives: $923 US
2. Converting 350 UK pounds to euro where 1 UK pound buys $.5071 euro
1. Commission: 5.25 pounds
2. Customer receives: 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) $5359.57
b) $7293.04
c) 9300.65 pounds
a. 113.40 euro
b. $1170.26
c. $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.
Calculating Repayment
1.
2.
3.
4.
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
total to be repaid
regular payment =
number of repayments
Repayment - Examples
Repayment - Examples
1. $274.84
2. 787.50 baht
3. $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.
𝐴 =𝐶 1+
𝑘𝑛
𝑟
100𝑘
= 450 1 +
(1)(4)
5
=
100(1)
$546.98