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Date	November 2021	Marks available	3	Reference code	21N.1.SL.TZ0.10
Level	Standard Level	Paper	Paper 1	Time zone	Time zone 0
Command term	Find	Question number	10	Adapted from	N/A

Question

In this question, give all answers correct to 2 decimal places.

Raul and Rosy want to buy a new house and they need a loan of $170 000$ Australian dollars ( $AUD$ ) from a bank. The loan is for $30$ years and the annual interest rate for the loan is $3.8 %$ , compounded monthly. They will pay the loan in fixed monthly instalments at the end of each month.

Find the amount they will pay the bank each month.

[3]

Find the amount Raul and Rosy will still owe the bank at the end of the first $10$ years.

[3]

b.i.

Using your answers to parts (a) and (b)(i), calculate how much interest they will have paid in total during the first $10$ years.

[3]

b.ii.

Markscheme

$N = 360$
$I % = 3.8$
$P V = (\pm) 170 000$
$F V = 0$
$P / Y = 12$
$C / Y = 12$ (M1)(A1)

Note: Award (M1) for an attempt to use a financial app in their technology with at least two entries seen, award A1 for all entries correct. Accept a positive or negative value for $P V$ .

$(P M T =) 792.13 AUD$ A1

Note: Accept an answer of $- 792.13$ . Do not award final A1 if answer is not given correct to $2$ dp.

[3 marks]

$N = 120$
$I % = 3.8$
$P V = (\pm) 170 000$
$P M T = (\mp) 792.13$
$P / Y = 12$
$C / Y = 12$ (M1)(A1)

Note: Award (M1) for an attempt to use a financial app in their technology with at least two entries seen, award A1 for all entries correct. $P V$ and $P M T$ must have opposite signs.

$(F V =) 133019.94 AUD$ A1

Note: Do not award final A1 if answer is not given correct to $2$ dp, unless already penalized in part (a). Accept $133020.30$ from use of exact value for $PMT$ .

[3 marks]

b.i.

amount of money paid: $120 \times 792.13 (= 95055.60)$ (M1)

loan paid off: $170 000 - 133019.94 (= 36980.06)$ (M1)

interest paid: $(95055.60 - 36980.06 =) 58075.54$ $AUD$ A1

Note: Allow $58075.60$ or $58075.90$ from use of some exact values from parts (a) and (b)(i). If their answer to part (b)(i) is greater than $170 000$ then award at most (M1)(M1)(A0) for follow through in part (b)(ii).

[3 marks]

b.ii.

Examiners report

This question was quite challenging for many candidates. In part (a), it was commendable that a significant minority of candidates arrived at the required answer, but others simply used $N = 30$ or attempted to use the compound interest formula. Candidates were not using their GDC efficiently. Those candidates who showed their calculator entries could score at least one mark out of three for communicating their method. For those candidates who were comfortable with the financial application in their GDC in parts (a) and (b)(i), five out of six marks was a popular score. Some neglected to round their answers to two decimal places as required. Part (c) proved to be particularly difficult for candidates to decipher which values were necessary to find the amount of interest paid. Most candidates scored only one mark for the amount of money paid over the ten years. Many incorrect or unnecessary calculations were shown. Some candidates attempted to find an interest rate.

b.i.

b.ii.

Syllabus sections

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

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