Accuracy penalty applies in part (c) if answer not given correct to 2 decimal places.

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1 Answers to Financial Math Review Packet-November Questions 1. Financial penalty (FP) applies in parts (b) and (d). Accuracy penalty applies in part (e) if answer not given correct to 2 decimal places (a) = (3880) (G2) Note: Award for multiplication of correct numbers. 3% of 4000 = = (3880) (G2) FP (b) = (ft)(g2) Note: Award for multiplication of correct numbers. Follow through from their answer to part (a). (c) = (1280) (G2) Note: Award for division of correct numbers. FP (d) (ft) Note: Follow through (their (c) ) (e) t = 1280 t = 4.94 (ft)(g2) Note: Follow through from their answers to parts (c) and (d). [9] 2. Financial penalty (FP) applies in part (b). Accuracy penalty applies in part (c) if answer not given correct to 2 decimal places. (a) 3.5 A = = = (AG) Notes: Award for substitution into correct formula, for correct substitution, for unrounded answer. If not seen award at most (A0) I = = A = = (AG) Note: Award for substitution into correct formula, for correct substitution, for unrounded answer. IB Questionbank Mathematical Studies 3rd edition 1

2 FP (b) Note: No follow through here. 0 3 r (c) = r = 3.66 (ft)(g2) Notes: Award for seen and used, for correct substitutions in simple interest formula, for answer. Follow through from their answer to (b). If or other is used as interest award at most (A0)(A0). [16] 3. Financial penalty (FP) applies in part (b). (a) k = = 1.29 (1 GBP = 1.29 EUR) (C2) Note: Accept 1.29 only (b) = EUR 2 % of = 5.06 EUR FP She receives EUR FP = EUR (C4) Note: Accept for 0.98 seen. 4. Financial penalty (FP) applies in part (b). ( 5000 r 4) (a) 568 = Note: Award for substitution into the simple interest formula, for correct values. r = 2.84 (C3) (b) I = 5000 (1.009) l Note: Award for substitution into the compound interest formula, for correct values. FP I = CHF (C3) IB Questionbank Mathematical Studies 3rd edition 2

3 5. Financial penalty (FP) applies in parts (a) and (c) in this question. (a) FP = (C2) Note: for multiplication by (b) = 75 (75.0, 75.00) If = 2.75 (C2) Note: Award (A0) (c) 2425 (ft) FP = (ft) (ft) FP = (ft) 3% of 91.8 = (ft) FP = (ft) (C2) Note: (ft) in (c) if the conversion process is reversed consistently through the question. i.e. multiplication in (a) followed by division in (c) 6. Financial penalty (FP) applies in part (a) in this question. (a) 2000(1.04) 10 Note: for substitution into CI formula. for correct substitution. FP Note: for substitution into CI formula for correct substitution 2960 (C3) (b) 1500(1.078) n = 3000 Note: for correct substitution in CI formula, for 3000 seen. IB Questionbank Mathematical Studies 3rd edition 3

4 n = 10 years (n = 9.23 years not accepted) 1500(1.078) n 1500 = 1500 Note: for correct substitution in CI formula, for 1500 seen. n = 10 years (n = 9.23 years not accepted) Note: (M2) for list or graph. n = 10 years (n = 9.23 years not accepted) (M2) Note: If simple interest formula is used in both parts (a) and (b) then award (M0)(M0)(A0) in (a) and 1500(7.8)n (b) 1500 = for substitution in SI formula or lists, for correct substitution n = 13 Correct answer only. (C3) If 9.23 seen without working award (A2). If calculator notation is used in either part with correct unrounded answer award (d) only if (FP) is applied in (a) or (AP) in (b). Otherwise (A2)(d) if penalty has already been applied in a previous question. 7. Financial penalty (FP) is applicable in question part (b) only. (a) Adam Crn I = Adam has = $8450 (C3) FP (b) Ben Amount = = $ (C3) Note: (A0) if interest only found (=$ ) 8. Financial accuracy penalty (FP) is applicable in parts (a) and (b). (a) = FP = euros (correct answer only) Note: First for 117 seen, for multiplying by 1.37 (G2) 3 IB Questionbank Mathematical Studies 3rd edition 4

5 13.5 (b) FP 9.85 GBP (answer correct to 2dp only) (ft)(g3) Note: First is for 13.5 seen, for dividing by (a) 3200 Swiss francs (C2) (b) (1.0125) Note: Award for formula with correct values. = Swiss francs Principal = Swiss francs. Note: for correct substituted formula, for correct values inserted. for and for adding back the The last follows through from the previous answer. (ft) (C4) (1.0125) 24 (M2) = Swiss francs Note: (M2) for correct substituted formula, for correct substitution, for correct answer. (M2) 10. (a) = Note: Award for multiplying by 0.98, for multiplying by Accept = = (C3) Note: for multiplying by 0.543, for multiplying by 0.02 and for correct answer (b) = 1.85 GBP Note: Award for , for subtracting 200 or for 2.5 seen and for correct answer in GBP. = 1.85 GBP (C3) IB Questionbank Mathematical Studies 3rd edition 5

6 Note: Award for subtracting from 150, for and for correct answer in GBP (a) for multiplying by = EUR (accept 1213) (C2) (b) / = (accept 780) (A2) (C3) (c) CAD (C1) (a) = (accept 669) 669 (G2) (C2) n (b) = 1200 n = 25.6 n = (G2) (C2) 20 r (c) = 1200 r 1 + = r = 3.53% 3.53% (G2) (C2) 13. (a) For attempting to find 5 years by compound interest formula or any alternative method. For using (1.0375) $ accept 3 s.f. (G3) Note: Accept $1440 or $1443. (b) For using answer in part (a) in an expression. For multiplying by (1.0325) 3 $ accept $1588 or $1590 (G3) IB Questionbank Mathematical Studies 3rd edition 6

7 14. (i) (a) Option Option (A3) 3 Notes: Award (A2) for Option 1 all correct. Award for Option 2 all correct. (b) A = 20000(1.035) 15 Option 1 = A = Option 2 = Option 1 = (G2) Option 2 = (G2) 4 (c) 7 years (from reading the table from GDC) (G2) (d) Note: Award for candidate s difference divided by their original times. = 2.56% 2 (ii) Option 3: (1.035) = $ Option 4: ( ) (1.035) 8 = $ $ (G3) $ (G3) She should choose Option 4 (R1) 7 [18] 15. (a) 2.95 euros (A2) (C2) (b) 3.40 euros % = = 2.04 euros 3.40 euros % = 2.04 euros (C3) IB Questionbank Mathematical Studies 3rd edition 7

8 (c) saving = 1.36 euros So, he must make 12 journeys. (C3) Note: If no working shown, award only (A2) for 11 journeys. ( ) 16. (a) Ali : 3000$3810 Note: Award for correct formula, for correct numbers in formula, for correct answer. 6 4 Bob : $ ( $ 3800) or (G3) 6 Note: Award for correct formula, for correct numbers in formula, for correct answer (b) Connie : $ (482) 200 Note: Award for correct formula, for correct numbers in formula for full correct answer. = $ (AG) 3 (c) 3000(1.04) 6000 n n n = 18 (by trial and error or solver or by using logarithms) or (G3) 3 (accept 17.7) (d) (i) 2% of = USD 2 (ii) = = GBP (accept , , 2620) 3 [17] 17. (a) = 1273 (A2) (C4) Note: Award for using correct formula, for substituting correct numbers, (A2) for answer ( of which is for answer to the nearest pound). Award (A0)(A2) ft if the candidate has put 3 for the power. Award (A0) ft if the candidate has put 1 for the power. 3% of 1200 = 36 IB Questionbank Mathematical Studies 3rd edition 8

9 (b) After 1 year fees = % of 1236 = fees after 2 years = = = 1273 Note: Award (A0) if candidate has repeated the process another time (1.03 1) (1.031) = (6370 to 3 s.f.) (A2) (C4) Note: Award for using correct formula, for substituting correct numbers, (A2) for answer. Candidates can also write out each term and add them up. Award for terms and (A2) for the correct answer. Award only if answer is incorrect due to premature rounding. 18. (a) (i) = Euros (492 Euros) (b) (ii) = Euros = GBP (103 GBP) (C5) = 3.08 (C3) 19. (a) A = 6000(1.06) 10 = (AUD) (C3) (b) = = = (to the nearest AUD) (C5) 20. (a) CHF (A2) (C2) (b) Method 1 2% of 0 CHF = 20 Amount = 0 20 = 980 CHF 980 = USD = USD = 554 USD (to nearest dollar) (C6) Method CHF = 1 USD IB Questionbank Mathematical Studies 3rd edition 9

10 0 0 CHF = 1.77 = = = 554 USD (to the nearest dollar) (ft from answer in (a)) (C6) 21. (a) 0.08 m f = 640 (A2) (C2) m + f = (A2) (C2) (b) 8 m + 6 f = m 8 f = f = (C2) f = 8000 or $8000 at First National Bank m = 2000 or $2000 at Midland Bank (C2) Note: Allow ft from part (a). 22. (a) S = 2.5(133 3) S = 325 CHF (C2) (b) S = 2.5(b 3) or 2.5(b 3) (A2) (C2) (c) 430 = 2.5(b 3) (M2) 172 = b = b 175 GBP (A2) (C4) 23. (a) Choice A = 12 = $ Choice B = = $ Choice C = = 12 { } $ Choice D = (1.05 1) = $ (1.05 1) Note: Award method marks if candidate works out each amount. But the answer has to be accurate to receive the mark of. 8 (b) Option D because the total allowance is the highest (C1) (R1) 2 2 (c) r = 1452 IB Questionbank Mathematical Studies 3rd edition 10

11 2 1 r = 1452 = r = = 1.1 r = 0.1 r = 10% (a) = 16 GBP Note: Penalize only once in parts (b) and (c) if the buying and selling price are consistently confused throughout the question. Allow (ft) marks. (b) = DM [14] (c) = DM = ( ) GBP = GBP (2 d.p.) Note: Penalize only once for answer not given to 2 d.p. [4] 25. (a) Amount End of month + Interest January February end January: = begin February: = end February: = (AG) 3 (b) March amount = = end of March = = April amount = = end of April = = (c) = (d) n = 3300 n = = n = = n = = Hence after 3 years n = 3300 n = 3, that is, after 3 years. (G2) 2 IB Questionbank Mathematical Studies 3rd edition 11

12 Note: Candidates may also use logarithms to solve this. [9] 26. (a) Monthly repayment = AUD (C1) (b) Monthly repayment on AUD 8000 taken over 5 years at 18% per annum = = AUD Note: Award for multiplying by 8 Total repaid = = AUD (C3) Notes: Award for multiplying by (5 12) or 60. No accuracy specified, but the answer is exact. [4] 27. (a) Price today = USD = USD = USD or US$ (to the nearest dollar) (C2) Note: Accept equivalent method (b) = 000 r = r 3 r = Rate = 6.00% per annum (3 s.f.) (accept 6%) (C2) [4] 28. Notes: If no method is shown, award if and only if answer is correct, otherwise award zero marks. However, award if correct method is shown; even if final answer is wrong. 1 (a) (i) p = = 1.56 (2 d.p.) (ii) q = = 5.26 (2 d.p.) Notes: For parts (a)(i) and (a)(ii) 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 (b) (i) GBP ( ) = GBP Note: Accept ( (or candidate s p)) = GBP (ii) (a) ( ) = GBP Note: Follow through from part (b)(i) above. IB Questionbank Mathematical Studies 3rd edition 12

13 (b) ( ) = GBP Note: Follow through from parts (b)(i) and (b)(ii)(a). (c) (i) 700(1.05) 4 = GBP Therefore interest = GBP (ii) 700(1.05) 5 = = (2 d.p.) 700(1.05) 6 = = (2 d.p.) therefore after 6 years 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) 2 [14] 29. (a) X(1.005) 12 (b) X(1.005) 12 r = X 1 Note: Award for equating follow through from (a). r = (1.0617) (or equivalent) Note: Award for isolating r correctly. Rate = 6.17% [4] 30. (a) Compound interest 8% per year (b) Year Value at beginning of year 1st CHF 500 CHF 540 Value at end of year 2nd CHF 540 CHF rd CHF CHF th CHF CHF th CHF CHF th CHF CHF [4] IB Questionbank Mathematical Studies 3rd edition 13

14 31. (a) (i) Cost of loan = 4000(1.01) = $ Note: Accept $ and then $4450 for part (b)(i) (ii) () Equivalent S.I. Rate = 4000 = = 12.7% (3 s.f.) 4 (b) (i) Deposit = 25% of $4000 = $0 (ii) Cost of the loan = (12) 3000 (or equivalent) = $ (c) (i) Option A. Because she doesn t need a deposit (or equivalent appropriate explanation). (R1) (ii) Option B. Because it is cheaper by $( ) = $57.30 (or equivalent appropriate explanation). (R1) 2 (d) x + 19y = 1540 x + 29y = 2140 x = 400 y = 60 4 (e) (n 1)60 = 4000 n = 61 Therefore, 61 months. 2 [15] IB Questionbank Mathematical Studies 3rd edition 14

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