IB Maths AI HL 1.4 Financial applications Question Bank

Practise IB Maths AI HL 1.4 through questions that extend financial models to annuities, changing periods, parameters and threshold decisions.

[Maximum number: 7]

Give your answers in parts (a), (d)(i), (e) and (f) to the nearest dollar.
Daisy invested 37000 Australian dollars (AUD) in a fixed deposit account with an annual interest rate of 6.4 % compounded quarterly.

(a)

Calculate the value of Daisy's investment after 2 years.

After m months, the amount of money in the fixed deposit account has appreciated to more than 50000 AUD.

[ 3 ]

EITHER
N=2
P V=-37000
I %=6.4
P / Y=1
C / Y=4
(M1)(A1)

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

OR
N=8
P V=-37000
I %=6.4
P / Y=4
C / Y=4

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

OR
$F V=37000 \times\left(1+\frac{6.4}{100 \times 4}\right)^{4 \times 2}$
(M1)(A1)

Note: Award M1 for substitution into compound interest formula, (A1) for correct substitution.
= 42010 AUD

Note: Award (M1)(A1)A0 for unsupported 42009.87.

(b)

Find the minimum value of m, where $m \in \mathbb{N}$ .

Daisy is saving to purchase a new apartment. The price of the apartment is 200000 AUD.
Daisy makes an initial payment of 25 % and takes out a loan to pay the rest.

[ 4 ]

EITHER
P V=-37000
F V=50000
I %=6.4
P / Y=1
C / Y=4
Note: Award M1 for an attempt to use a financial app in their technology, award A1 for all entries correct. The final mark can still be awarded for the correct number of months (multiple of 3 ).
OR
P V=-37000
F V=50000
I %=6.4
P / Y=4
C / Y=4
Note: Award M1 for an attempt to use a financial app in their technology, award A1 for all entries correct.
OR

50000<37000 \times\left(1+\frac{6.4}{100 \times 4}\right)^{4 \times n} \text { OR } 50000<37000 \times\left(1+\frac{6.4}{100 \times 4}\right)^{n} \quad \text { (M1)(A1) }

Note: Award M1 for the correct inequality, 50000 and substituted compound interest formula. Allow an equation. Award A1 for correct substitution.

THEN

\begin{aligned} & N=4.74(\text { years })(4.74230 \ldots) \text { OR } N=18.9692 \ldots \text { (quarters) } \\ & m=57 \text { months } \end{aligned}

Note: Award A1 for rounding their m to the correct number of months. The final answer must be a multiple of 3 . Follow through within this part.

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SL 1.4—Financial applications question 1

Question (a)

Question (b)