math studies financial maths

ECOLE MONDIALE WORLD SCHOOL MUMBAI Mathematical Studies SL Assessment on Financial Mathematics Max.Marks: 90 Name:_______________________________________ 1.

Susi travels from Singapore to Thailand and changes 1500 Singapore dollars (SGD) to Thai baht (THB). The exchange rate is 1 SGD buys 21.03464 THB. (a)

Calculate the number of Thai baht Susi buys. Give your answer correct to the nearest baht. (2)

Susi leaves Thailand and travels to Indonesia. She has 20 000 THB and uses these to buy Indonesian rupiah (IDR). The exchange rate is 3.28352 THB buys 1000 IDR. (b)

Calculate the total number of Indonesian rupiah Susi receives, correct to the nearest thousand rupiah. (2)

Susi wants to find the approximate exchange rate between Singapore dollars and Indonesian rupiah and uses the exchange rates for Thai baht to do this. (c)

Calculate Susi’s exchange rate between Singapore dollars and Indonesian rupiah. Give your answer in the form 1 SGD buys x IDR, where x is given correct to the nearest rupiah. (2) (Total 6 marks)

2.

Inge borrows € 4500 for 2 years. (a)

Bank 1 charges compound interest at a rate of 15 % per annum, compounded quarterly. Calculate the total amount to be repaid at the end of the 2 years. Give your answer correct to two decimal places. (3)

(b)

Bank 2 charges simple interest, and Inge would repay the same total amount as for Bank 1. Find the rate of interest charged by Bank 2. (3) (Total 6 marks)

IB Questionbank Mathematical Studies 3rd edition

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3. Jane plans to travel from Amsterdam to Chicago. She changes 1500 Euros (EUR) to US Dollars (USD) at an exchange rate of 1 EUR to 1.33 USD. Give all answers in this question correct to two decimal places. (a)

Calculate the number of USD Jane receives. (1)

Jane spends 1350 USD and then decides to convert the remainder back to EUR at a rate of 1 EUR to 1.38 USD. (b)

Calculate the amount of EUR Jane receives. (3)

If Jane had waited until she returned to Amsterdam she could have changed her USD at a rate of 1 EUR to 1.36 USD but the bank would have charged 0.8% commission. (c)

Calculate the amount of EUR Jane gained or lost by changing her money in Chicago. (2) (Total 6 marks)


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4.

The table below shows some exchange rates for the Japanese Yen (JPY). Currency

1 JPY

Canadian Dollar

0.010406

Chinese Yuan

0.07127

Euro

0.0072591

Norwegian Kroner

0.057319

Minbin has 1250 Japanese Yen which she wishes to exchange for Chinese Yuan. (a)

Calculate how many Yuan she will receive. Give your answer to the nearest Yuan. (2)

Rupert has 855 Canadian Dollars which he wishes to exchange for Japanese Yen. (b)

Calculate how many Yen he will receive. Give your answer to the nearest Yen. (2)

(c)

Find how many Norwegian Kroner there are to the Euro. Give your answer correct to 2 decimal places. (2) (Total 6 marks)

5.

Mario has spent $40000 to buy some land. The land increases in value by 5% each year. (i)

What is the value of the land after the end of five years?

At the end of five years, Mario sells the land. He pays 1% tax on the sale and spends the rest of the money on a car. The car loses value at a rate of $2500 every year. (ii)

How much tax does Mario pay?

(iii)

How much is the car worth five years after Mario buys it? (Total 8 marks)


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6.

Give all answers in this question to the nearest whole currency unit. In January 2008 Larry had 90 000 USD to invest for his retirement in January 2011. He invested 40 000 USD in US government bonds which paid 4 % per annum simple interest. (a)

Calculate the value of Larry’s investment in government bonds in January 2011. (3)

Larry changed this investment into South African rand (ZAR) at an exchange rate of 1 USD = 18.624 ZAR. (b)

Calculate the amount that Larry received in ZAR from the exchange. (2)

He changed the remaining 50 000 USD to South African rand (ZAR) in January 2008. The exchange rate between USD and ZAR was 1 USD = 10.608 ZAR. There was 2.5 % commission charged on the exchange. (c)

Calculate the value, in USD, of the commission Larry paid. (2)

(d)

Show that the amount that Larry had to invest is 517 000 ZAR, correct to the nearest thousand ZAR. (3)

In January 2008, Larry deposited this money into a bank account that paid interest at a nominal annual rate of 12 %, compounded monthly. (e)

Find the value of the money in Larry’s bank account in January 2011. (3) (Total 13 marks)


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7.

The following is a currency conversion table: FFR

USD

JPY

GBP

French Francs (FFR)

1

p

q

0.101

US Dollars (USD)

6.289

1

111.111

0.631

Japanese Yen (JPY)

0.057

0.009

1

0.006

British Pounds (GBP)

9.901

1.585

166.667

1

For example, from the table 1 USD = 0.631 GBP. Use the table to answer the following questions. (a)

Find the values of p and q. (2)

(b)

Mireille wants to change money at a bank in London. (i)

How many French Francs (FFR) will she have to change to receive 140 British Pounds (GBP)?

(ii)

The bank charges a 2.4% commission on all transactions. If she makes this transaction, how many British Pounds will Mireille actually receive from the bank? (4)

(c)

Jean invested 5000 FFR in Paris at 8% simple interest per annum. Paul invested 800 GBP in London at 6% simple interest per annum. (i)

How much interest in FFR did Jean earn after 4 years?

(ii)

How much interest in US Dollars did Paul earn after 4 years?

(iii)

Who had earned more interest after 4 years?

(iv)

Explain your reasoning in part (c) (iii). (7) (Total 13 marks)


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8.

Give all your numerical answers correct to two decimal places. On 1 January 2005, Daniel invested 30 000 AUD at an annual simple interest rate in a Regular Saver account. On 1 January 2007, Daniel had 31 650 AUD in the account. (a)

Calculate the rate of interest. (3)

On 1 January 2005, Rebecca invested 30 000 AUD in a Supersaver account at a nominal annual rate of 2.5 % compounded annually. (b)

Calculate the amount in the Supersaver account after two years. (3)

(c)

Find the number of complete years since 1 January 2005 it will take for the amount in Rebecca’s account to exceed the amount in Daniel’s account. (3)

On 1 January 2007, Daniel reinvested 80 % of the money from the Regular Saver account in an Extra Saver account at a nominal annual rate of 3 % compounded quarterly. (d)

(i)

Calculate the amount of money reinvested by Daniel on the 1 January 2007.

(ii)

Find the number of complete years it will take for the amount in Daniel’s Extra Saver account to exceed 30 000 AUD. (5) (Total 14 marks)


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9.

(i)

Celia has $20,000 to invest. There are two different options from which she can choose. Option 1: The investment grows at a rate of 3.5% compound interest each year. Option 2: The total value of the investment increases by $800 each year. The money is to be invested for 15 years. (a)

Complete the table below giving the values of the investments to the nearest dollar for the first 4 years. (3)

(b)

Year

0

1

Option 1

20 000

20 700

Option 2

20 000

20 800

2

3

4

Calculate the values of each investment at the end of 15 years. (4)

(c)

If Option 1 is chosen find the total number of complete years before the value of the investment is first greater than $25,000. (2)

(d)

If Option 2 is chosen calculate the percentage increase in the investment for the final year. (2)

(ii)

Two more Options are available to Celia. After 7 years she can change the investment conditions. Option 3: If Celia has chosen Option 1 she can change and then receives $800 each year until the end of the 15 years. Option 4: If Celia has chosen Option 2 she can change and then receive 3.5% interest compounded annually. If Celia wishes to receive the maximum amount of money at the end of the 15 years which option should she choose? (7) (Total 18 marks)


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math studies financial maths

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