Calculate correct to 2 decimal places the amount of euros he receives. (3) He buys 1 kilogram of Belgian chocolates at 1.35 euros per 100 g.
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1 1. Robert, who lives in the UK, travels to Belgium. The exchange rate is 1.37 euros to one British Pound (GBP) with a commission of 3 GBP, which is subtracted before the exchange takes place. Robert gives the bank 120 GBP. Calculate correct to 2 decimal places the amount of euros he receives. He buys 1 kilogram of Belgian chocolates at 1.35 euros per 100 g. Calculate the cost of his chocolates in GBP correct to 2 decimal places. 2. At what interest rate, compounded annually, would you need to invest $100 in order to have $125 in 2 years? (Total 4 marks) 3. 1 Brazilian Real (BRL) = South African Rand (ZAR). Giving answers correct to two decimal places, (i) convert 300 BRL to ZAR; find how many Real it costs to purchase 300 Rand. Marilia deposits a gift of 150 Real from her aunt into a savings account. The savings account pays an annual simple interest rate of r. The interest is added to the account at the end of each month. After 9 months, the amount in the savings account was Real. Find the value of r. IB Questionbank Mathematical Studies 3rd edition 1
2 4. 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. 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. Calculate the amount of EUR Jane receives. 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. 5. Two brothers Adam and Ben each inherit $6500. Adam invests his money in a bond that pays simple interest at a rate of 5 per annum. Ben invests his money in a bank that pays compound interest at a rate of 4.5 per annum. Calculate the value of Adam s investment at the end of 6 years. Calculate the value of Ben s investment at the end of 6 years. Give your answer correct to 2 decimal places. IB Questionbank Mathematical Studies 3rd edition 2
3 6. Emma places 8000 in a bank account that pays a nominal interest rate of 5 per annum, compounded quarterly. Calculate the amount of money that Emma would have in her account after 15 years. Give your answer correct to the nearest Euro. After a period of time she decides to withdraw the money from this bank. There is in her account. Find the number of months that Emma had left her money in the account. 7. The following table shows the monthly payments needed to repay a loan of $1000 with various rates and time periods. Table of Monthly Repayments per $1000 Annual interest rate Loan Term (months) 5% 5.5% 6% 6.5% Sarah takes out a personal loan for $ to buy a car. She negotiates a loan for three years at 6 per annum interest. Calculate the exact monthly repayment she will make. Find the exact total of the repayments she will make. Beryl took out a loan of $ for 18 months. The total she paid for the loan was $ (c) Find the rate of interest charged on the loan. IB Questionbank Mathematical Studies 3rd edition 3
4 8. John invests X USD in a bank. The bank s stated rate of interest is 6% per annum, compounded monthly. Write down, in terms of X, an expression for the value of John s investment after one year. What rate of interest, when compounded annually (instead of monthly) will give the same value of John s investment as in part? Give your answer correct to three significant figures. (Total 4 marks) 9. The table shows part of a currency conversion chart. For example GBP 1 is equivalent to FFR GBP USD FFR GBP 1 p 8.33 USD q FFR l For all calculations in this question give your answers correct to two decimal places. Calculate the value of (i) p; q. (4) Joe has USD 1500 to exchange at a bank. (i) Assuming no commission is charged, how much in GBP will Joe receive from the bank? Assuming the bank charges 1.5% commission, how much in GBP does Joe pay in commission? (1) IB Questionbank Mathematical Studies 3rd edition 4
5 how much in GBP does Joe actually receive for his USD 1500? (1) (c) Joe decides to invest GBP 700 of his money in a savings account which pays interest at 5%, compounded annually. (i) How much interest will the GBP 700 earn after 4 years? For how many years must Joe invest his GBP 700 in order to earn at least GBP 200 in interest? (d) After 4 years Joe has a total of GBP 900 in his savings account on an investment at 5% interest compounded annually. How much did he invest? Give your answer to the nearest one GBP. (Total 14 marks) 10. Angela needs $4000 to pay for a car. She was given two options by the car seller. Option A: Outright Loan A loan of $4000 at a rate of 12% per annum compounded monthly. Find (i) the cost of this loan for one year; the equivalent annual simple interest rate. Option B: Friendly Credit Terms A 25% deposit, followed by 12 equal monthly payments of $ (i) How much is to be paid as a deposit under this option? (1) Find the cost of the loan under Friendly Credit Terms. IB Questionbank Mathematical Studies 3rd edition 5
6 (c) Give a reason why Angela might choose (i) Option A Option B To help Angela, her employer agrees to give her an interest free loan of $4000 to buy the car. The employer is to recover the money by making the following deductions from Angela s salary: $x in the first month, $y every subsequent month. The total deductions after 20 months is $1540 and after 30 months it is $2140. (d) Find x and y. (4) (e) How many months will it take for Angela to completely pay off the $4000 loan? (Total 15 marks) 11. Financial accuracy penalty (FP) is applicable in parts and = (A1) FP = euros (correct answer only) Note: First (A1) for 117 seen, for multiplying by 1.37 (A1)(G2) (A1) 3 FP 9.85 GBP (answer correct to 2dp only) (A1)(ft)(G3) Note: First (A1) is for 13.5 seen, for dividing by 1.37 IB Questionbank Mathematical Studies 3rd edition 6
7 r 12. A = C r 125 = r 1.25 = r = 100 r = 11.8% (3 s.f.) n 2 2 (A1) (C4) [4] 13. Financial accuracy penalty (FP) is applicable where indicated. 1 BRL = ZAR FP (i) = ZAR (A1) Note: is (A0)(FP) FP BRL (A1)(ft) (C2) Note: Follow through only if processes are reversed. Time period is Interest is r 8.1or r = 7.2 (A1) (A1) (A1) (C4) Notes: Award (A1) for 3 seen. Award (A1) for 8.1 seen. 4 3 Award for the equation with or 9 and either 8.1 or There is no follow through in part. IB Questionbank Mathematical Studies 3rd edition 7
8 14. Financial penalty (FP) may apply in this question FP = (accept 1995) (A1) (C1) USD left = = 645 (A1) = 645 Euros (A1)(ft) 1.38 FP = Euros (A1)(ft) (C3) 645 (c) (A1)(ft) 1.36 FP She lost 3.08 Euros (A1)(ft) Notes: If candidate has divided in and multiplied in and (c) consistently award (A0)(A1)(ft)(A1)(ft) for answers of for USD left and Euros in and (A1)(ft)(A1)(ft) for and 6.86 in (c). (C2) 15. Financial penalty (FP) is applicable in question part only. Adam Crn I 100 = Adam has = $8450 (A1) (A1) (C3) FP Ben Amount = (A1) 100 = $ (A1) (C3) Note: (A1)(A0) if interest only found (=$ ) 16. FV = 8000 (1.0125) 60 (A1) Note: for substituting in compound interest formula, (A1) for correct substitution only (A1) (C3) 8000 (1.0125) n = IB Questionbank Mathematical Studies 3rd edition 8
9 Note: for equating compound interest formula to n =10 correct answer only (A1) So 30 months, (ft) on their n Note: Award (C2) for 2.5 seen with no working (A1)(ft) (C3) 17. Financial penalty (FP) may apply in this question (A1) Note: (A1) for seen FP = $ (A1) (C2) Note: For multiplying their by 36. Can be implied. FP = $ (A1)(ft) (C2) (c) = Rate = 5.5 (A1) (C2) 18. X(1.005) 12 (A1) X(1.005) 12 r = X Note: Award for equating follow through from. r = 100(1.0617) 100 (or equivalent) Note: Award for isolating r correctly. Rate = 6.17% (A1) [4] IB Questionbank Mathematical Studies 3rd edition 9
10 19. Notes: If no method is shown, award (A1) if and only if answer is correct, otherwise award zero marks. However, award if correct method is shown; even if final answer is wrong. (i) p = q = = 1.56 (2 d.p.) (A1) 1 = 5.26 (2 d.p.) (A1) Notes: For parts (i) and accept and follow through with conversions routed via candidate s home currency. For example: USD 1 = GBP 0.64 GBP 1 = FFR 8.33 USD 1 = FFR (0.64) (8.33) q = 5.33 instead of 5.26 (i) GBP ( ) = GBP (A1) 2 Note: Accept ( (or candidate s p)) = GBP ( ) = GBP (A1) 1 Note: Follow through from part (i) above. ( ) = GBP (A1) 1 Note: Follow through from parts (i) and. (c) (i) 700(1.05) 4 = GBP Therefore interest = GBP (A1) 2 700(1.05) 5 = = (2 d.p.) 700(1.05) 6 = = (2 d.p.) therefore after 6 years (A1) 2 Note: Accept other correct methods. (d) C(1.05) 4 = C = 4 (1.05) Notes: Award the at the point where C has been correctly isolated 900 Accept C = = GBP = GBP 740 (nearest GBP) (A1) 2 [14] IB Questionbank Mathematical Studies 3rd edition 10
11 20. (i) Cost of loan = 4000(1.01) = $ (A1) Note: Accept $ and then $4450 for part (i) (100) Equivalent S.I. Rate = 4000 = = 12.7% (3 s.f.) (A1) 4 (i) Deposit = 25% of $4000 = $1000 (A1) Cost of the loan = (12) 3000 (or equivalent) = $ (A1) 3 (c) (i) Option A. Because she doesn t need a deposit (or equivalent appropriate explanation). (R1) Option B. Because it is cheaper by $( ) = $57.30 (or equivalent appropriate explanation). (R1) 2 (d) x + 19y = 1540 x + 29y = 2140 x = 400 (A1) y = 60 (A1) 4 (e) (n 1)60 = 4000 n = 61 Therefore, 61 months. (A1) 2 [15] IB Questionbank Mathematical Studies 3rd edition 11
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