IB Math Studies

Topic 8 – Financial Math: Exchange rates

Buying and selling rates

Exchange rates at First Cape Bank

$1 US Buying Selling

£ 0.65 0.62

Euro 1.10 1.06

Aus $ 1.95 1.88

Yen 98 96

First note the difference between the buying and the selling rates. This is how the bank makes part of it’s profit.

If a customer has US$200 and she wants Euro:

If a customer has 5000 Yen and he wants US$:

Use the selling price.

Use the buying price.

Using exchange rates

Exchange rates at First Cape Bank

$1 US Buying Selling

£ 0.65 0.62

Euro 1.10 1.06

Aus $ 1.95 1.88

Yen 98 96

1. Lidia is going on holiday to Australia. She is taking US$1200 as spending money.

a) Calculate how many Aus$ will she have when she exchanges all her US$.

b) On returning to the US she has Aus$250 left. How many US$ will she have after exchanging them at the bank?

2. Sam arrives in the US with £460 and exchanges all this with the bank into US$. How many US$ will he have?

460 0.65 $707.69

Commission rates

Banks may also charge a commission rate, this is a sum for performing the exchange.

This could be a fixed charge or as a percentage charge of the exchange rate.

Fixed rate

The First Bank offers an exchange rate of £1=$1.64 with a fixed rate of £5 per transaction. Calculate how many $ you would receive for £350.

Percentage charge

The Seconds Bank offers an exchange rate of £1=$1.66 with a commission rate of 2.2%. Calculate how many $ you would receive for £350.

Questions

1. Convert £300 into $ at a rate of £1=$1.56 with a fixed commission rate of £5.

2. A bank exchanges $ at a commission rate of 1.5%.Convert $500 into Yen at a rate of $1=95 Yen.

3. A bank buys Euros at $0.9 and sells at $0.86. Calculate how many Euros a customer with $400 will receive.

4. Convert $300 into £ if $1=£0.68 and the bank charges $3 commission.

5. A bank buys $ for £1=0.59 and sells for £1=0.57, with a 1.7% commission charge.Alfie has £870, how many $ will he receive?

344 Euros

£201.96

$1449.50

Practice

page 457 (Exercise 15A.1)page 460 (Exercise 15A.2)page 462 (Exercise 15A.3)