| Date | May 2015 | Marks available | 3 | Reference code | 15M.1.sl.TZ1.10 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Calculate | Question number | 10 | Adapted from | N/A |
Question
Pierre invests 5000 euros in a fixed deposit that pays a nominal annual interest rate of 4.5%, compounded monthly, for seven years.
Calculate the value of Pierre’s investment at the end of this time. Give your answer correct to two decimal places.
Carla has 7000 dollars to invest in a fixed deposit which is compounded annually.
She aims to double her money after 10 years.
Calculate the minimum annual interest rate needed for Carla to achieve her aim.
Markscheme
\(5000{\left( {1 + \frac{{4.5}}{{12 \times 100}}} \right)^{12 \times 7}}\) (M1)(A1)
Note: Award (M1) for substitution into compound interest formula, (A1) for correct substitutions.
OR
\(N = 7\)
\(I\% = 4.5\)
\(PV = ( \pm )5000\)
\(P/Y = 1\)
\(C/Y = 12\) (A1)(M1)
Note: Award (A1) for \(C/Y = 12\) seen, (M1) for all other correct entries.
OR
\(N = 84\)
\(I\% = 4.5\)
\(PV = ( \pm )5000\)
\(P/Y = 12\)
\(C/Y = 12\) (A1)(M1)
Note: Award (A1) for \(C/Y = 12\) seen, (M1) for all other correct entries.
\( = 6847.26{\text{ (euros)}}\) (A1) (C3)
Note: Answer must be correct to 2 decimal places for the final (A1) to be awarded.
\(14000 = 7000{\left( {1 + \frac{r}{{100}}} \right)^{10}}\) (M1)(A1)
Notes: Award (M1) for substitution into compound interest formula equated to 14000 or equivalent.
Award (A1) for correct substitutions.
OR
\(N = 10\)
\(PV = \pm 7000\)
\(FV \mp 14000\)
\(P/Y = 1\)
\(C/Y = 1\) (A1)(M1)
Note: Award (A1) for \(C/Y = 1\) seen, (M1) for other correct entries. \(PV\) and \(FV\) must have opposite signs.
\(r = 7.18\% \;\;\;(7.17734 \ldots \% ,{\text{ }}0.0718)\) (A1) (C3)
Note: Do not penalize if \(\%\) sign is missing. Do not accept \(0.0718\%\).
Examiners report
Many correct answers were given for part (a). Incorrect answers were in most cases the result of incorrect substitution into the compound interest formula, or incorrect use of the calculator, both in using the formula or when using the finance application. A common mistake was the use of 0.045 instead of 4.5 for r in the formula.
In part (b) a correct equation was often given, but an analytical or graphical solution was rarely found. When the finance application of the GDC was used candidates often found the correct answer.
