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Date	November Example question	Marks available	2	Reference code	EXN.1.SL.TZ0.9
Level	Standard Level	Paper	Paper 1	Time zone	Time zone 0
Command term	Hence and Find	Question number	9	Adapted from	N/A

Question

Sophia pays $$ 200$ into a bank account at the end of each month. The annual interest paid on money in the account is $3.1 %$ which is compounded monthly.

The average rate of inflation per year over the $5$ years was $2 %$ .

Find the value of her investment after a period of $5$ years.

[3]

a.

Find an approximation for the real interest rate for the money invested in the account.

[2]

b.

Hence find the real value of Sophia’s investment at the end of $5$ years.

[2]

c.

Markscheme

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

Number of time periods $12 \times 5 = 60$ (A1)

N = $60$
I% = $3.1$
PV = $0$
PMT = $200$
P/Y = $12$
C/Y = $12$
Value $($) 12, 961.91$ (M1)A1

[3 marks]

a.

METHOD 1

Real interest rate $= 3.1 - 2.0 = 1.1 %$ (M1)A1

METHOD 2

$\frac{1 + 0.031}{1 + 0.02} = 1.01078 \dots$ (M1)

$1.08 %$ (accept $1.1 %$ ) A1

[2 marks]

b.

N = $60$
I% = $1.1$
PV = $0$
PMT = $200$
P/Y = $12$
C/Y = $12$
$($) 12, 300 (12, 330.33 \dots)$ (M1)A1

Note: Award A1 for $$ 12, 300$ only.

[2 marks]

c.

Examiners report

[N/A]

a.

[N/A]

b.

[N/A]

c.

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