| Date | May 2018 | Marks available | 3 | Reference code | 18M.1.sl.TZ2.5 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Calculate | Question number | 5 | Adapted from | N/A |
Question
In this question, give all answers to two decimal places.
Karl invests 1000 US dollars (USD) in an account that pays a nominal annual interest of 3.5%, compounded quarterly. He leaves the money in the account for 5 years.
Calculate the amount of money he has in the account after 5 years.
Write down the amount of interest he earned after 5 years.
Karl decides to donate this interest to a charity in France. The charity receives 170 euros (EUR). The exchange rate is 1 USD = t EUR.
Calculate the value of t.
Markscheme
\(1000{\left( {1 + \frac{{3.5}}{{4 \times 100}}} \right)^{4 \times 5}}\) (M1)(A1)
Note: Award (M1) for substitution in compound interest formula, (A1) for correct substitution.
OR
N = 5
I = 3.5
PV = 1000
P/Y = 1
C/Y = 4
Note: Award (A1) for C/Y = 4 seen, (M1) for other correct entries.
OR
N = 5 × 4
I = 3.5
PV = 1000
P/Y = 1
C/Y = 4
Note: Award (A1) for C/Y = 4 seen, (M1) for other correct entries.
= 1190.34 (USD) (A1)
Note: Award (M1) for substitution in compound interest formula, (A1) for correct substitution.
[3 marks]
190.34 (USD) (A1)(ft) (C4)
Note: Award (A1)(ft) for subtraction of 1000 from their part (a)(i). Follow through from (a)(i).
[1 mark]
\(\frac{{170}}{{190.34}}\) (M1)
Note: Award (M1) for division of 170 by their part (a)(ii).
= 0.89 (A1)(ft) (C2)
Note: Follow through from their part (a)(ii).
[2 marks]
