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Date November 2019 Marks available 3 Reference code 19N.1.SL.TZ0.T_8
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Calculate Question number T_8 Adapted from N/A

Question

Siân invests 50000 Australian dollars (AUD) into a savings account which pays a nominal annual interest rate of 5.6 % compounded monthly.

Calculate the value of Siân’s investment after four years. Give your answer correct to two decimal places.

[3]
a.

After the four-year period, Siân withdraws 40000 AUD from her savings account and uses this money to buy a car. It is known that the car will depreciate at a rate of 18 % per year.

The value of the car will be 2500 AUD after t years.

Find the value of t.

[3]
b.

Markscheme

FV=50000(1+5.6100×12)12×4       (M1)(A1)

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

 

OR

N=4

I%=5.6

PV=()50000

P/Y=1

C/Y=12        (A1)(M1)

Note: Award (A1) for C/Y=12 seen, (M1) for all other correct entries.

 

OR

N=48

I%=5.6

PV=()50000

P/Y=12

C/Y=12        (A1)(M1)

Note: Award (A1) for C/Y=12 seen, (M1) for all other correct entries.

 

(FV=)62520.97 (AUD)        (A1)    (C3)

Note: The final (A1) is not awarded if the answer is not correct to 2 decimal places.

[3 marks]

a.

2500=40000(118100)t   OR  2500=40000(0.82)t1       (M1)(A1)

Note: Award (M1) for substitution into compound interest formula or term of a geometric sequence formula and equating to 2500, (A1) for correct substitution.

 

OR

I%=18

PV=(±)40000

FV=()2500

P/Y=1

C/Y=1        (A1)(M1)

Note: Award (A1) for FV=()2500 seen, (M1) for all other correct entries. PV and FV must have opposite signs.

 

OR

328002689622054.7218084.8714829.59       (M1)

t13=3031.38  and  t14=2485.73        (A1)

Note: Award (M1) for a list of at least 5 correct terms beginning with 32800, (A1) for identifying t13 and t14.

(t=) 14.0 (13.9711)        (A1)    (C3)

 

[3 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

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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