| Date | May 2018 | Marks available | 3 | Reference code | 18M.2.sl.TZ1.3 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Calculate | Question number | 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.
Calculate 14 000 USD in INR.
Calculate the amount of this investment, in INR, in this account after five years.
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.
Markscheme
\(17500 = 14000{\left( {1 + \frac{r}{{100}}} \right)^5}\) (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.
OR
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.
OR
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.
OR
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]
