Financial Math Lesson #1
Foreign Exchange
• When you are in another country you must use the currency of
that country. This means that you must exchange your money
for the equivalent amount of local currency (money). The
equivalent amount is found using exchange rates.
• Exchange rates show the relationship between the values of
currencies. They are published daily in newspapers, in bank
windows and on the internet at various bank and travel agency
sites.
• Exchange rates change constantly. The
table to the right is an example of a typical
newspaper currency exchange table.
• It shows how much $1 Australian is worth
in some other currencies.
• The exchange rates in any country are
usually given as the amount of foreign
currency equal to one unit of the local
currency.
• For example, suppose you are from Europe with 800 euro and
you travel to India. You need to know how many Indian rupee
there are to 1 euro. From an Indian exchange table similar to
this one, we might find that 1 euro = 55.376 rupee .
• So, your 800 euro will buy 800 × 55.376 rupee = 44300 rupee .
• Example 1:
Given that 1 South African rand = $0.2754 Singapore, find
how many Singapore dollars you could buy for 2500 South
African rand.
1 South African rand = $0.2754 Singapore
2500 South African rand = 2500 × $0.2754 Singapore
= $688.50 Singapore
• Notice that both buying and selling rates at the bank are
included in the table. These two quantities differ as the bank
makes a profit on all money exchanges.
Buying And Selling International Currency
• Selling
o How much foreign currency will you receive by selling
other currency?
o Use the selling exchange rate and the formula:
Foreign currency bought
= other currency sold × selling exchange rate
o Example 1:
Given that $1 Australian = 0.4032 UK pounds (when
selling), convert $500 Australian into United Kingdom
pounds.
UK currency bought = 500 × 0.4032 pounds
= 201.60 pounds
o How much will it cost you in your currency if you have to
purchase foreign currency?
o You are selling your currency, so use the selling
exchange rate and the formula:
foreign currency bought
Cost in currency you have =
selling exchange rate
o Example 2:
What does it cost in New Zealand dollars to buy $2000
US, if $1 NZ = 0.6328 US?
cost in $ NZ =
2000
$3160.55 US
0.6328
• Buying
o You have currency from another country and want to
change it to your country’s currency. You are buying
your currency. Use the buying exchange rate and:
foreign currency sold
Your currency bought =
buying exchange rate
o Example:
If you have $1000 Hong Kong and exchange it for
Phillipine pesos, how many pesos will you receive if
1 peso = $0.1454 HK?
1000
6880 pesos
0.1454
• Conversion graphs are line graphs which enable us to convert
from one quantity to another.
• Example:
The graph to the right shows the
relationship between Australian
dollars and English pounds on a
particular day.
Find:
(a.) the number of dollars in 250
pounds
(b.) the number of pounds in 480
dollars
(c.) whether a person with $360
could afford to buy an item valued
at 200 pounds.
Pesos bought =
(a.) 250 pounds is equivalent to $600.
(b.) $480 is equivalent to 200 pounds.
(c.) $360 is equivalent to 150 pounds.
Therefore, they cannot afford to buy the item.
Commission On Currency Exchange
• When any currency trader (such as a bank) exchanges
currency for a customer a commission is paid by the customer
1
for this service. The commission could vary from % to 3% .
2
• The commission could be calculated using
o a fixed percentage
o the buy/sell values.
• Example 1:
A bank charges US dollars to other currency at a fixed
commission of 1.5%. Max wishes to convert $200 US to baht
where $1 US buys 40.23 Thai baht.
(a.) What commission is charged?
(b.) What does the customer receive?
(a.) Commission
(b.) customer receives
= $200 US × 1.5%
197 × 40.23 baht
= $200 US × 0.015
7925 baht
= $3 US
• Example 2:
A currency exchange service exchanges 1 euro for Japanese
Yen using: ‘buy at 135.69, sell at 132.08’. Cedric wishes to
exchange 800 euro for Yen.
(a.) How many Yen will he receive?
(b.) If the Yen in (a.) is converted immediately back to euro,
how many euro are bought?
(c.) What is the resultant commission on the double
transaction?
(a.) Cedric receives
800 × 132.08 105700 Yen
(using the selling rate as the bank is selling currency)
(b.) Cedric receives
105700
779 euro
135.69
(using the buying rate as the bank is buying currency)
(c.) The resultant commission is 800 − 779 = 21 euro .
Travellers Cheques
• When travelling overseas some people carry their money as
travellers cheques. They are more convenient than carrying
large amounts of cash. They provide protection in case of
accidental loss or theft. If necessary travellers cheques may be
quickly replaced.
• Travellers cheques are usually purchased from a bank before
you leave your country. You should take the currency of the
country you are visiting or a widely acceptable currency like US
dollars. Usually banks who provide travellers cheques charge
1% of the value of the cheques when they are issued.
• So,
amount of foreign currency
cos t of travellers cheques =
× 101%
selling exchange rate
• Note: It is also possible to buy foreign currency using a credit
card that is accepted internationally, such as Visa or
Mastercard. Currency can be purchased using your credit cards
at banks and automatic teller machines (ATMs) in most
countries.
• Example:
If you want to buy 2000 UK pounds worth of travellers cheques,
what will it cost in Australian dollars, if $1 Australian = 0.4032
pounds?
cos t =
2000
× 1.01 = $5009.90 Australian
0.4032
Simple Interest
• Under this method, interest is calculated on the full amount
borrowed or lent for the entire period of the loan or investment.
• For example,
o if $2000 is borrowed at 8% p.a. for 3 years, the interest
payable for 1 year is 8% of $2000 = $2000 × 0.08
o So, for 3 years it would be ($2000 × 0.08) × 3
• From examples like this one we construct the simple interest
formula.
• This is I = C × r × n where:
o I, is the $ amount of interest
o C, is the principal (amount borrowed)
o r, is the simple interest per annum as a decimal
o n, is the time (or length) of the loan, and is always
expressed in terms of years.
• Example 1:
Calculate the simple interest on a loan of $8000 at a rate of 7%
p.a. over 18 months.
C = 8000 , r = 0.07 , n =
18
= 1.5
12
Now,
I = C×r ×n
So,
I = 8000 × 0.07 × 1.5
Therefore, I = 840
i.e., simple interest is $840.
• We can also use the same formula to find the other three
variables C, r, and n in the equation.
• Example 2:
How much is borrowed if a rate of 6.5% p.a. simple interest
results in an interest charge of $3900 after 5 years?
I = 3900 , r = 0.065 , n = 5
Now,
I = C×r ×n
So,
3900 = C × 0.065 × 5
Therefore, C = 12000
i.e., $12000 was borrowed.
• Example 3:
If you wanted to earn $6000 in interest on a 4 year loan of
$18000, what rate of simple interest would you need to charge?
I = 6000 , C = 18000 , n = 4
I = C×r ×n
Now,
6000 = 18000 × r × 4
So,
Therefore, r = 0.083333 = 0.083333 × 100% = 8.3333%
1
i.e., the simple interest rate is 8 % p.a.
3
• Example 4:
How long would it take to earn interest of $4760 on a loan of
$16000 if a rate of 8.5% p.a. simple interest is charged?
I = 4760 , C = 16000 , r = 0.085
I = C×r ×n
Now,
4760 = 16000 × 0.085 × n
So,
Therefore, n = 3.5
1
i.e., it would take 3 years to earn $4760 in interest.
2
Calculating Repayments
• Whenever money is borrowed, the amount borrowed (or
principal) must be repaid along with the interest charges
applicable to that loan. In addition, it must be repaid within the
loan period. The full amount of the repayment can be made
either by:
o making one payment on a set date at the conclusion of
the loan period, or
o making numerous (usually equal) periodic payments
over the loan period.
• When the loan is repaid by making equal periodic payments
over the loan period, the amount of each periodic payment is
calculated by dividing the total to be repaid by the number of
payments to be made,
principal + int erest
C +I
Periodic repayment =
i.e., Rp =
number of repayments
N
• Example:
1
Calculate the monthly repayments on a loan of $7000 at 8 %
2
p.a. simple interest over 4 years.
Step 1:
Calculate interest
C = 7000
r = 0.085
n=4
Now, I = C × r × n
I = 7000 × 0.085 × 4
I = 2380
i.e., interest is $2380.
Step 2:
Calculate repayments
C = 7000
I = 2380
N = 4 × 12 = 48 months
C + I 7000 + 2380
Rp =
=
Now,
N
48
Therefore, Rp = 195.42
i.e., monthly repayments of $195.42 are needed.