Grade 11 Maths · Financial Maths

Convert nominal and effective rates

Change between a yearly quoted rate and the real yearly rate, for example 12% a year compounded monthly is about 12,68% effective.

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Financial Maths Grade 11 | Effective to NominalKevinmathscience

04 Effective and nominal interest ratesWiskunde_Mathematics_SUM

Grade 11 Financial Mathematics: Effective and Nominal Interest RateMaths Matters

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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.

More past paper questions: convert nominal and effective rates

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3. Question 8.2.1 · November 2024 · Paper 1 · Provincial · 4 marks
8.2 Koza deposits R15 000 into a bank account for a period of 10 years. The interest rate for the first four years is 6% per annum compounded monthly. For the next six years, the interest rate changes to 10% per annum compounded semi-annually.

Answer the questions that follow.
8.2.1 Convert the nominal rates to annual effective rates. (Answers correct to FOUR decimal places)(4)
Show the memo (4 ticks)Memo
1. ✓
  Formula with values (6% monthly) $i_{e ff} = (1 + \frac{0 , 06}{12})^{12} - 1$
  1 mark · Convert nominal and effective rates
2. ✓
  $6, 1678%$ $= 6, 1678%$
  1 mark · Convert nominal and effective rates
3. ✓
  Formula with values (10% semi-annually) $i_{e ff} = (1 + \frac{0 , 1}{2})^{2} - 1$
  1 mark · Convert nominal and effective rates
4. ✓
  $10, 25%$ $= 10, 25%$
  1 mark · Convert nominal and effective rates
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 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
6. 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

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