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Date	May 2018	Marks available	3	Reference code	18M.2.SL.TZ1.T_3
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 1
Command term	Calculate	Question number	T_3	Adapted from	N/A

Question

Give your answers to parts (b), (c) and (d) to the nearest whole number.

Harinder has 14 000 US Dollars (USD) to invest for a period of five years. He has two options of how to invest the money.

Option A: Invest the full amount, in USD, in a fixed deposit account in an American bank.

The account pays a nominal annual interest rate of r % , compounded yearly, for the five years. The bank manager says that this will give Harinder a return of 17 500 USD.

Option B: Invest the full amount, in Indian Rupees (INR), in a fixed deposit account in an Indian bank. The money must be converted from USD to INR before it is invested.

The exchange rate is 1 USD = 66.91 INR.

The account in the Indian bank pays a nominal annual interest rate of 5.2 % compounded monthly.

Calculate the value of r.

[3]

Calculate 14 000 USD in INR.

[2]

Calculate the amount of this investment, in INR, in this account after five years.

[3]

Harinder chose option B. At the end of five years, Harinder converted this investment back to USD. The exchange rate, at that time, was 1 USD = 67.16 INR.

Calculate how much more money, in USD, Harinder earned by choosing option B instead of option A.

[3]

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$17500 = 14000{\left( {1 + \frac{r}{{100}}} \right)^5}$ (M1)(A1)

Note: Award (M1) for substitution into the compound interest formula, (A1) for correct substitution. Award at most (M1)(A0) if not equated to 17500.

N = 5

PV = ±14000

FV = $\mp$ 17500

P/Y = 1

C/Y = 1 (A1)(M1)

Note: Award (A1) for C/Y = 1 seen, (M1) for all other correct entries. FV and PV must have opposite signs.

= 4.56 (%) (4.56395… (%)) (A1) (G3)

[3 marks]

14000 × 66.91 (M1)

Note: Award (M1) for multiplying 14000 by 66.91.

936740 (INR) (A1) (G2)

Note: Answer must be given to the nearest whole number.

[2 marks]

$936740 \times {\left( {1 + \frac{{5.2}}{{12 \times 100}}} \right)^{12 \times 5}}$ (M1)(A1)(ft)

Note: Award (M1) for substitution into the compound interest formula, (A1)(ft) for their correct substitution.

N = 60

I% = 5.2

PV = ±936740

P/Y= 12

C/Y= 12 (A1)(M1)

Note: Award (A1) for C/Y = 12 seen, (M1) for all other correct entries.

N = 5

I% = 5.2

PV = ±936740

P/Y= 1

C/Y= 12 (A1)(M1)

Note: Award (A1) for C/Y = 12 seen, (M1) for all other correct entries

= 1214204 (INR) (A1)(ft) (G3)

Note: Follow through from part (b). Answer must be given to the nearest whole number.

[3 marks]

$\frac{{1214204}}{{67.16}}$ (M1)

Note: Award (M1) for dividing their (c) by 67.16.

$\left( {\frac{{1214204}}{{67.16}}} \right) - 17500 = 579$ (USD) (M1)(A1)(ft) (G3)

Note: Award (M1) for finding the difference between their conversion and 17500. Answer must be given to the nearest whole number. Follow through from part (c).

[3 marks]

Examiners report

[N/A]

Syllabus sections

Topic 1—Number and algebra » SL 1.4—Financial apps – compound interest, annual depreciation

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