IB Maths AA SL 1.4 Financial applications Question Bank

Practise IB Maths AA SL Financial applications with SL questions that develop route-specific sequence or financial reasoning and exam accuracy.

[Maximum number: 4]

Give your answers to parts (a)(ii), (c)(i) and (d) correct to two decimal places.
Daniela and Sorin have each recently received some money. Daniela won a cash prize and Sorin received an inheritance.
Daniela had two options to choose from to receive her winnings. In both options she receives a payment on the first day of each month for three years.
Option A Each payment is $ 5500.
Option B The first payment is $ 2000. In each month which follows, the payment is 6 % more than the previous month.

(a)

Write down an expression for the value of Sorin's investment after n years.

Daniela chose Option B and received her first payment on $1^{\text {st }}$ January 2023. Sorin invested his inheritance on the same day.

[ 1 ]

Sorin's future value after n years $=120000\left(1+\frac{4}{100 \times 12}\right)^{12 n}$

(b)

Find the value of r if this investment grows to $ 53000 after six years.

[ 3 ]

EITHER
N=24
OR
N=6
$\mathrm{PV}=\mp 40000$ $\mathrm{PV}=\mp 40000$
PMT=0
PMT=0
$\mathrm{FV}= \pm 53000$ $\mathrm{FV}= \pm 53000$
P / Y=4
P / Y=1
C / Y=4
C / Y=4
(M1)(A1)
Note: Award (M1) for an attempt to use a financial app in their technology with at least two entries seen, and award (A1) for all entries correct. PV and FV must have opposite signs.

OR
$40000\left(1+\frac{r}{100 \times 4}\right)^{6 \times 4}=53000$
(M1)(A1)

Note: Award (M1) for attempting to substitute into compound interest formula, award (A1) for correct equation.

THEN
$4.71781 \ldots$
( r= ) 4.72 (\%)

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SL 1.4—Financial applications question 1

Question (a)

Question (b)