Financial Maths: Interest, Hire Purchase & Exchange Rates

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FREE CAPS MATHS RESOURCES

Grade 9 · Financial Maths

MARKING GUIDELINE

Marks

Duration

55 minutes

Questions

Name:

Class:

Date:

Mark

/ 34

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
R8 000 is invested at 9% p.a. SIMPLE interest for 4 years. The interest is …
(1)
A)R2 880✓
B)R720
C)R10 880
D)R11 292,65
Answer: A — I = P × r × n = 8 000 × 0,09 × 4.
- B — that is ONE year's interest
- C — that is the total VALUE, not the interest
- D — that is the COMPOUND total
1.2
R8 000 at 9% p.a. COMPOUND interest for 4 years grows to …
(1)
A)R10 880
B)R11 292,65✓
C)R2 880
D)R8 720
Answer: B — A = 8 000(1,09)⁴.
- A — that is the SIMPLE interest total
- C — that is the simple interest alone
- D — that is one year only
1.3
Compound interest is larger than simple interest because …
(1)
A)the rate is higher
B)interest is earned ON the interest already added✓
C)it is calculated monthly
D)the period is longer
Answer: B — Each year's interest joins the balance and earns interest itself.
- A — the rate is the same in both
- C — compounding can be yearly too
- D — the period is the same in both
1.4
A car worth R180 000 depreciates at 12% p.a. on the STRAIGHT-LINE method. After 3 years it is worth …
(1)
A)R122 693,76
B)R115 200✓
C)R64 800
D)R126 000
Answer: B — A = 180 000(1 − 0,12 × 3) = 180 000(0,64).
- A — that is REDUCING-BALANCE depreciation
- C — that is the amount LOST, not the value left
- D — used one year only
1.5
A shop offers hire purchase: 10% deposit on R5 000 and 12 instalments of R420. The TOTAL paid is …
(1)
A)R5 040
B)R5 540✓
C)R5 000
D)R500
Answer: B — Deposit R500 + 12 × R420 = R5 040, so R5 540.
- A — left the deposit out
- C — that is the cash price
- D — that is the deposit alone
1.6
R1 = 18,50 South African rand. How many rand is $250?
(1)
A)R13,51
B)R4 625✓
C)R268,50
D)R231,50
Answer: B — 250 × 18,50 = 4 625.
- A — divided instead of multiplying
- C — added instead of multiplying
- D — subtracted instead of multiplying
1.7
A salesperson earns 6% commission on sales of R45 000. The commission is …
(1)
A)R7 500
B)R2 700✓
C)R270
D)R42 300
Answer: B — 0,06 × 45 000 = 2 700.
- A — divided by 6 instead of multiplying
- C — used 0,6%
- D — that is the sales less the commission
1.8
VAT at 15% on a price of R2 400 excluding VAT gives a total of …
(1)
A)R2 415
B)R2 760✓
C)R2 086,96
D)R360
Answer: B — 2 400 × 1,15 = 2 760.
- A — added 15 rands instead of 15 per cent
- C — REMOVED VAT instead of adding it
- D — that is the VAT alone
1.9
Which formula gives COMPOUND interest?
(1)
A)A = P(1 + in)
B)A = P(1 + i)ⁿ✓
C)A = P(1 − in)
D)A = P(1 − i)ⁿ
Answer: B — The exponent n is what compounds the growth.
- A — that is SIMPLE interest
- C — that is straight-line depreciation
- D — that is reducing-balance depreciation
1.10
A budget shows income R9 500 and expenses R10 200. The household should …
(1)
A)spend more
B)reduce expenses by at least R700✓
C)save R700
D)borrow R9 500
Answer: B — Expenses exceed income by R700.
- A — that makes the deficit worse
- C — there is nothing spare to save
- D — borrowing the whole income is not the shortfall

Answer grid — marking guideline

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[12 MARKS]

Answer the questions below. Round all money off to the nearest cent.

2.1
Calculate the simple interest on R4 000 invested at 9% per annum for 3 years.
(3)
I = P × i × n = 4 000 × 0,09 × 3 (2) = R1 080 (1)
2.2
Calculate the amount when R10 000 is invested at 5% per annum compound interest for 2 years, and state how much MORE it earns than simple interest at the same rate.
(5)
A = 10 000(1,05)² = R11 025 (2)
Simple: 10 000(1 + 0,05 × 2) = R11 000 (2)
Compound earns R25 more (1)
2.3
Carol invests R18 000 for 6 years at 15% per annum compounded annually. Calculate the value of her investment at the end.
(4)
A = P(1 + i)ⁿ (1)
= 18 000(1,15)⁶ (2) = R41635,09 (1)

Question 3

[12 MARKS]

Answer the questions below.

3.1
A television costs R9 000 cash. On hire purchase a 15% deposit is paid. Calculate the deposit and the balance owing.
(3)
Deposit = 0,15 × 9 000 = R1 350 (2)
Balance = R7 650 (1)
3.2
Brian wants to exchange rands for British pounds. R1 is worth 0,075199 pounds. Calculate how many pounds he receives for R2 100 BEFORE commission.
(3)
2 100 × 0,075199 (2) = £157,92 (1)
3.3
The agent charges 1,5% commission on the transaction. Calculate how many pounds Brian actually receives, correct to TWO decimal places.
(4)
He keeps 98,5% of the pounds (1)
157,92 × 0,985 (2) = £155,55 (1)
3.4
Explain why hire purchase costs more in total than paying cash.
(2)
Interest is charged on the outstanding balance (1), so the instalments add up to more than the cash price (1)

TOTAL: 34 marks

This question paper consists of 3 questions.