Simple & Compound Interest: Every Exam Type — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 10 · Financial Maths

Simple & Compound Interest: Every Exam Type

MARKING GUIDELINE

Marks

Duration

50 minutes

Questions

Name:

Class:

Date:

Mark

/ 32

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
R5 000 is invested at 8% p.a. SIMPLE interest for 3 years. The final amount is …
(1)
A)R6 200✓
B)R6 298,56
C)R1 200
D)R5 400
Answer: A — A = P(1 + ni) = 5 000(1 + 0,24) = R6 200.
- B — used the COMPOUND formula P(1 + i)ⁿ
- C — that is the INTEREST earned, not the final amount
- D — worked out one year only
1.2
R5 000 is invested at 8% p.a. COMPOUND interest for 3 years. The final amount is …
(1)
A)R6 298,56✓
B)R6 200
C)R1 298,56
D)R5 400
Answer: A — A = P(1 + i)ⁿ = 5 000(1,08)³ = R6 298,56.
- B — used the SIMPLE interest formula
- C — that is the INTEREST earned, not the final amount
- D — compounded for one year only
1.3
Compound interest earns more than simple interest because …
(1)
A)interest is earned on the interest already added✓
B)the interest rate is higher
C)the period is longer
D)the principal is larger
Answer: A — Each year the interest is worked out on a balance that has already grown.
- B — the rate is the same in both cases
- C — the period is the same in both cases
- D — the principal is the same in both cases
1.4
R20 000 is invested at 6% p.a. compounded for 5 years. The INTEREST earned is …
(1)
A)R6 764,51✓
B)R26 764,51
C)R6 000
D)R1 200
Answer: A — A = 20 000(1,06)⁵ = R26 764,51, so the interest is A − P = R6 764,51.
- B — that is the final AMOUNT, not the interest
- C — used simple interest: 20 000 × 0,06 × 5
- D — worked out one year's interest only
1.5
What principal grows to R12 000 in 4 years at 10% p.a. SIMPLE interest?
(1)
A)R8 571,43✓
B)R7 200
C)R8 196,16
D)R4 800
Answer: A — P = A ÷ (1 + ni) = 12 000 ÷ 1,4 = R8 571,43.
- B — MULTIPLIED by 0,6 instead of dividing by 1,4
- C — used the COMPOUND formula, dividing by (1,1)⁴
- D — worked out the interest instead of the principal
1.6
A car worth R180 000 depreciates at 12% p.a. on the STRAIGHT-LINE method. After 3 years it is worth …
(1)
A)R115 200✓
B)R122 665
C)R64 800
D)R158 400
Answer: A — A = P(1 − ni) = 180 000(1 − 0,36) = R115 200.
- B — used the reducing-balance formula P(1 − i)ⁿ
- C — worked out the value LOST rather than the value left
- D — depreciated for one year only
1.7
Inflation runs at 6% p.a. Something costing R500 today will cost … in 3 years.
(1)
A)R595,51✓
B)R590
C)R530
D)R95,51
Answer: A — A = 500(1,06)³ = R595,51.
- B — used simple growth, 500(1 + 0,18)
- C — grew the price for one year only
- D — that is the INCREASE, not the new price
1.8
At what SIMPLE interest rate does R4 000 grow to R5 200 in 5 years?
(1)
A)6% p.a.✓
B)30% p.a.
C)5,4% p.a.
D)23,1% p.a.
Answer: A — The interest is R1 200, and 1 200 = 4 000 × r × 5 gives r = 0,06.
- B — forgot to divide by the 5 years
- C — used the COMPOUND formula instead of the simple one
- D — divided by the final AMOUNT instead of the principal, and dropped the years
1.9
Interest compounded MONTHLY at 12% p.a. for 2 years uses …
(1)
A)i = 0,01 and n = 24✓
B)i = 0,12 and n = 2
C)i = 0,12 and n = 24
D)i = 0,01 and n = 2
Answer: A — Divide the annual rate by 12 and multiply the number of years by 12.
- B — those are the ANNUAL values, which ignore the monthly compounding
- C — adjusted the periods but left the rate annual
- D — adjusted the rate but left the number of periods at 2
1.10
R10 000 at 9% p.a. compounded for 4 years, correct to the NEAREST RAND, is …
(1)
A)R14 116✓
B)R13 600
C)R10 900
D)R14 115,82
Answer: A — A = 10 000(1,09)⁴ = R14 115,82, which is R14 116 to the nearest rand.
- B — used simple interest, 10 000(1 + 0,36)
- C — compounded for one year only
- D — the value is right, but the question asks for the nearest RAND

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

[11 MARKS]

Determine THROUGH CALCULATION which of the two investments below is more profitable.
• R7 000 at 10% p.a. COMPOUND interest for 5 years
• R7 000 at 12% p.a. SIMPLE interest for 5 years

2.1
Calculate the value of the compound-interest investment after 5 years.
(3)
A = P(1 + i)ⁿ = 7 000(1,1)⁵ (2) = R11 273,57 (1)
2.2
Calculate the value of the simple-interest investment after 5 years.
(3)
A = P(1 + in) = 7 000(1 + 0,12 × 5) (2) = R11 200 (1)
2.3
State which investment is more profitable and by how much.
(3)
The compound investment (1)
R11 273,57 − R11 200 (1) = R73,57 more (1)
2.4
Explain why the compound investment wins despite its LOWER interest rate.
(2)
Compound interest is calculated on the growing balance (1), so it earns interest on interest, while simple interest is always worked out on the original R7 000 (1)

Question 3

[11 MARKS]

Samson buys a television and a DVD player for R12 800. He pays R2 200 in cash and the balance through a hire-purchase agreement at 15% p.a. simple interest, repaid over two years.

3.1
Calculate the amount of the loan.
(2)
12 800 − 2 200 (1) = R10 600 (1)
3.2
Calculate the total amount that must be repaid on the loan.
(3)
A = 10 600(1 + 0,15 × 2) (2) = R13 780 (1)
3.3
Calculate Samson's monthly repayment.
(3)
Over 24 months: 13 78024 (2) = R574,17 (1)
3.4
Determine how much MORE than the cash price of R12 800 Samson pays in total.
(3)
Total paid = 2 200 + 13 780 = R15 980 (2)
15 980 − 12 800 = R3 180 (1)

TOTAL: 32 marks

This question paper consists of 3 questions.