Grade 11 Maths · Financial Maths · Paper 1

Effects of Different Compounding Periods Grade 11

Real Effects of Different Compounding Periods past paper questions and answers from 2023 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

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Question 7.1 · May/June 2025 · Paper 1 · National (DBE) · 2 marks

7.1 John invests an amount of money in an account paying interest at a rate of

15%

p.a., compounded monthly. Calculate the annual effective interest rate of this investment.(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

Effects of Different Compounding Periods skills

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More Effects of Different Compounding Periods Grade 11 questions and answers

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4. Question 8.1 · November 2023 · Paper 1 · Provincial · 3 marks
8.1 Calculate the effective interest rate per annum if an investment earns interest at a rate of $9, 3%$ p.a. compounded monthly.(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula $1 + i_{e ff} = (1 + \frac{i _{n o m}}{m})^{m}$
  1 mark · Convert nominal and effective rates
2. ✓
  Substitution $i_{e ff} = (1 + \frac{0 , 093}{12})^{12} - 1$
  1 mark · Convert nominal and effective rates
3. ✓
  Answer $= 0, 09707$
  $= 9, 71%$
  1 mark · Convert nominal and effective rates
5. Question WE15 · Siyavula Grade 11 Mathematics, 9.4 Nominal and effective interest rates, Worked example 15 · 3 marks
WE15 Interest on a credit card is quoted as $23%$ p.a. compounded monthly. What is the effective annual interest rate? Give your answer correct to two decimal places.(3)
Show the memo (3 ticks)Memo
1. ✓
  FormulaInterest is added monthly: $m = 12$ ; $i^{(12)} = 0, 23$
  $1 + i = (1 + \frac{i ^{(m)}}{m})^{m}$
  1 mark · Convert nominal and effective rates
2. ✓
  Substitution $1 + i = (1 + \frac{0 , 23}{12})^{12}$
  1 mark · Convert nominal and effective rates
3. ✓
  Answer $∴ i = (1 + \frac{0 , 23}{12})^{12} - 1 = 25, 59%$
  The effective interest rate is $25, 59%$ per annum.
  1 mark · Convert nominal and effective rates
6. Question WE16 · Siyavula Grade 11 Mathematics, 9.4 Nominal and effective interest rates, Worked example 16 · 3 marks
WE16 Determine the nominal interest rate compounded quarterly if the effective interest rate is $9%$ per annum (correct to two decimal places).(3)
Show the memo (3 ticks)Memo
1. ✓
  FormulaInterest is added quarterly: $m = 4$ ; $i = 0, 09$
  $1 + i = (1 + \frac{i ^{(m)}}{m})^{m}$
  1 mark · Convert nominal and effective rates
2. ✓
  Substitution $1 + 0, 09 = (1 + \frac{i ^{(4)}}{4})^{4}$
  1 mark · Convert nominal and effective rates
3. ✓
  Answer $4 1, 09 = 1 + \frac{i ^{(4)}}{4}$
  $4 (4 1, 09 - 1) = i^{(4)}$
  $∴ i^{(4)} = 8, 71%$
  The nominal interest rate is $8, 71%$ p.a. compounded quarterly.
  1 mark · Convert nominal and effective rates

Effects of Different Compounding Periods Grade 11 videos

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Compounding monthly grade 11 | Financial MathsKevinmathscience

Financial Maths Grade 11 | Effective to NominalKevinmathscience

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