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Date May 2021 Marks available 3 Reference code 21M.2.SL.TZ1.3
Level Standard Level Paper Paper 2 Time zone Time zone 1
Command term Find Question number 3 Adapted from N/A

Question

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.

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

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.

The loan is for 10 years, compounded monthly, with equal monthly payments of 1700 AUD made by Daisy at the end of each month.

For this loan, find

After 5 years of paying off this loan, Daisy decides to pay the remainder in one final payment.

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

[3]
a.

Find the minimum value of m, where m.

[4]
b.

Write down the amount of the loan.

[1]
c.

the amount of interest paid by Daisy.

[2]
d.i.

the annual interest rate of the loan.

[3]
d.ii.

Find the amount of Daisy’s final payment.

[3]
e.

Find how much money Daisy saved by making one final payment after 5 years.

[3]
f.

Markscheme

EITHER

N=2
PV=-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
PV=-37000
I%=6.4
P/Y=4
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

FV=37000×1+6.4100×44×2              (M1)(A1)


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

 

=42010 AUD          A1


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


[3 marks]

a.

EITHER

PV=-37000
FV=50000
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. The final mark can still be awarded for the correct number of months (multiple of 3).


OR

PV=-37000
FV=50000
I%=6.4
P/Y=4
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

50000<37000×1+6.4100×44×n  OR  50000<37000×1+6.4100×4n            (M1)(A1)


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

 

THEN

N=4.74  years 4.74230  OR  N=18.9692  quarters            (A1)

m=57 months          A1


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.


[4 marks]

b.

150000 AUD        A1

 

[1 mark]

c.

120×1700-150000        (M1)

=54000 AUD        A1

 

[2 marks]

d.i.

N=120
PV=-150000
PMT=1700
FV=0
P/Y=12
C/Y=12        (M1)(A1)


Note: Award M1 for an attempt to use a financial app in their technology or an attempt to use an annuity formula or FV=0 seen. If a compound interest formula is equated to zero, award M1, otherwise award M0 for a substituted compound interest formula.
Award A1 for all entries correct in financial app or correct substitution in annuity formula, but award A0 for a substituted compound interest formula. Follow through marks in part (d)(ii) are contingent on working seen.

 

r=6.46 %  6.45779        A1

 

[3 marks]

d.ii.

N=60
I=6.46  6.45779
PV=-150000
PMT=1700
P/Y=12
C/Y=12        (M1)(A1)


Note: Award M1 for an attempt to use a financial app in their technology or an attempt to use an annuity formula. Award (M0) for a substituted compound interest formula. Award A1 for all entries correct. Follow through marks in part (e) are contingent on working seen.

 

FV=86973 AUD        A1

 

[3 marks]

e.

204000-60×1700+86973  OR  204000-188973       (M1)(A1)


Note: Award M1 for 60×1700. Award M1 for subtracting their 60×1700+86973 from their (204000). Award at most M1M0 for their 204000-60×1700 or M0M0 for their 204000-86973. Follow through from parts (d)(i) and (e). Follow through marks in part (f) are contingent on working seen.

 

=15027 AUD        A1

 

[3 marks]

f.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.i.
[N/A]
d.ii.
[N/A]
e.
[N/A]
f.

Syllabus sections

Topic 1—Number and algebra » SL 1.4—Financial apps – compound interest, annual depreciation
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Topic 1—Number and algebra

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