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Date	May 2021	Marks available	3	Reference code	21M.1.SL.TZ2.10
Level	Standard Level	Paper	Paper 1	Time zone	Time zone 2
Command term	Calculate	Question number	10	Adapted from	N/A

Question

Tommaso and Pietro have each been given $1500$ euro to save for college.

Pietro invests his money in an account that pays a nominal annual interest rate of $2.75 %$ , compounded half-yearly.

Calculate the amount Pietro will have in his account after $5$ years. Give your answer correct to $2$ decimal places.

[3]

Tommaso wants to invest his money in an account such that his investment will increase to $1.5$ times the initial amount in $5$ years. Assume the account pays a nominal annual interest of $r %$ compounded quarterly.

Determine the value of $r$ .

[3]

Markscheme

METHOD 1

$N = 5$ OR $N = 10$
$I % = 2.75$ $I % = 2.75$
$P V = - 1500$ $P V = - 1500$
$P M T = 0$ $P M T = 0$
$P / Y = 1$ $P / Y = 2$
$C / Y = 2$ $C / Y = 2$ (M1)(A1)

Note: Award M1 for an attempt to use a financial app in their technology, A1 for all entries correct.

METHOD 2

$1500 {(1 + \frac{2.75}{2 \times 100})}^{2 \times 5}$ (M1)(A1)

$1719.49$ euro A1

[3 marks]

METHOD 1

$N = 5$ OR $N = 20$
$P V = \pm 1500$    $P V = \pm 1500$
$F V = \mp 2250$    $F V = \mp 2250$
$P M T = 0$ $P M T = 0$
$P / Y = 1$ $P / Y = 4$
$C / Y = 4$ $C / Y = 4$   (M1)(A1)

Note: Award M1 for an attempt to use a financial app in their technology, A1 for all entries correct. $P V$ and $F V$ must have opposite signs.

METHOD 2

$1500 {(1 + \frac{r}{4 \times 100})}^{4 \times 5} = 2250$ OR ${(1 + \frac{r}{4 \times 100})}^{4 \times 5} = 1.5$ (M1)(A1)

Note: Award M1 for substitution in compound interest formula, A1 for correct substitution and for equating to $2250$ (if using LHS equation) or to $1.5$ (if using RHS equation).

$r = 8.19 (8.19206 \dots)$ A1

Note: Accept $r = 8.19 %$ .

Accept a trial and error method which leads to $r = 8.19$ .

[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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