Finance: Growth & Decay (Grade 11) — Worksheet & Memo

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Grade 11 · Finance, Growth and Decay

Finance: Growth & Decay (Grade 11)

MEMORANDUM

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/ 38

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
R15 000 is invested at 8% p.a. compounded annually. Calculate the value after 5 years.
(3)
15 000(1,08)⁵ = R22 039,92✓✓✓ (3)
2
R15 000 is invested at 8% p.a. compounded monthly. Calculate the value after 5 years.
(3)
15 000(1 + 0,08/12)⁶⁰ = R22 347,69✓✓✓ (3)
3
A fridge has a cash price of R9 200. On hire purchase a 20% deposit is paid and the balance is repaid over 2 years at 14% p.a. simple interest. Calculate the TOTAL amount paid. (hire purchase revision)
(4)
Deposit = 0,20 × 9 200 = R1 840; loan = R7 360; A = 7 360(1 + 0,14 × 2) = 7 360 × 1,28 = R9 420,80; total = 1 840 + 9 420,80 = R11 260,80✓✓✓✓ (4)
4
How much MORE than its cash price does that fridge cost on hire purchase? (hire purchase revision)
(2)
11 260,80 − 9 200 = R2 060,80 — which is exactly the interest, 7 360 × 0,28✓✓ (2)
5
A car worth R240 000 depreciates at 15% p.a. on a straight line. Calculate its value after 4 years.
(3)
240 000(1 − 0,6) = R96 000✓✓✓ (3)
6
A car worth R240 000 depreciates at 15% p.a. on a reducing balance. Calculate its value after 4 years.
(3)
240 000(0,85)⁴ = R125 281,50✓✓✓ (3)
7
Convert 8% p.a. compounded monthly to an effective annual rate.
(3)
(1 + 0,08/12)¹² − 1 = 8,30%✓✓✓ (3)
8
A loaf of bread costs R18. If inflation is 6% p.a., what will it cost in 8 years?
(3)
18(1,06)⁸ = R28,69✓✓✓ (3)
9
R50 000 grows to R80 000 in 6 years at compound interest, compounded annually. Calculate the annual interest rate.
(4)
80 000 = 50 000(1 + i)⁶ → (1 + i)⁶ = 1,6
1 + i = 1,6^1/6 = 1,0815
i = 0,0815 → 8,15% p.a.✓✓✓✓ (4)
10
State the difference between a nominal and an effective interest rate.
(2)
The nominal rate is the advertised annual rate before compounding; the effective rate is the true annual rate once compounding within the year is included.✓✓ (2)
11
The rate moves from R18,20 to R19,60 to the dollar. Has the rand strengthened or weakened, and what happens to the price of imported goods?
(2)
Weakened ✓ (more rands are needed per dollar); imported goods become more expensive ✓(2)
12
A camera costs $340. Calculate its cost in rands at R18,75 to the dollar, and then at R20,10 to the dollar.
(3)
340 × 18,75 = R6 375 ✓; 340 × 20,10 = R6 834 ✓; an increase of R459 ✓(3)
13
Explain why the petrol price can rise in South Africa even when the international oil price has not changed.
(3)
Oil is priced in dollars ✓; if the rand weakens, more rands are needed to buy the same dollar amount of oil ✓, so the pump price rises without the oil price moving ✓(3)

TOTAL: 38 marks