O-LevelMathematicsNumber4024/21 · May/June 2021 · Q19 Marks

In 2019 Nicole's annual income was $22000.

(a)She spent $7200 on accommodation in 2019. Calculate the percentage of her income she spent on accommodation.[2]
(b)Her annual income of $22000 increased by 4% in 2020. Calculate her annual income in 2020.[2]
(c)(i)Nicole invests $2000 in an account. The account pays compound interest at a rate of K% per year. At the end of the first year, the money in the account is $2036. Show that K = 1.8.[2]
(c)(ii)Find the number of complete years before Nicole has at least $2150 in the account. Show your working.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

[2] 32.7 or 32.72 to 32.73
[2] 22 880
[M1] 2000(1+K/100) = 2036 soi
[A1] leading to K = 1.8 A0 for any incorrect working
[3] 5 with 2147 to 2148 and 2186 to 2187
[3] or 5 with (1+1.8/100)^n = 1.075 and 1.073 to 1.074 and 1.093 to 1.094
[3] or 5 with 4.05 or 4.053 to 4.054
[3] M2 for [2000] (1+1.8/100)^4 oe or [200] (1+1.8/100)^5 oe or 1.018^n = 1.075 or M1 for 2000 (1+1.8/100)^n oe where n > 1

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