Grade 10 Maths · Financial Maths

Use the compound interest formula

Use the compound interest formula A = P(1 + i)ⁿ, where interest also earns interest, for example R1 000 at 10% for 2 years grows to R1 210.

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Financial Maths Grade 10 | Compound Interest | IntroductionKevinmathscience

2) Compound Interest Grade 9 | Part 1Kevinmathscience

Financial Maths Grade 11 | Simple and Compound RevisionKevinmathscience

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Question 7.1 · November 2024 · Paper 1 · National (DBE) · 3 marks

7.1 Mary's grandparents deposited R5 000 into a savings account on the day that she was born. The account pays interest at a rate of 6,8% p.a., compounded quarterly. Calculate the accumulated amount in this account on Mary's

1 6^{th}

birthday.(3)

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

More past paper questions: use the compound interest formula

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3. Question 7.3 · May/June 2025 · Paper 1 · National (DBE) · 6 marks
7.3 On 1 March 2021, Abby made a once-off deposit of $R 12000$ into an account earning interest at a rate of $9, 5%$ p.a., compounded monthly. She deposited $R 500$ into the same account on 1 April 2023 and continues to make these monthly deposits of $R 500$ on the first day of each month thereafter. Calculate how much money was in the account immediately after the deposit of $R 500$ is made on 1 March 2025, exactly four full years after her initial deposit.(6)
Show the memo (6 ticks)Memo
1. ✓
  Identify the monthly interest rate $r_{i} = \frac{0 , 095}{12}$
  1 mark · Find i and n per period
2. ✓
  Identify the number of compounding periods for the initial once-off depositFrom 1 March 2021 to 1 March 2025 is exactly 4 years.
  $n = 12 \times 4 = 48$ months.
  1 mark · Find i and n per period
3. ✓
  Calculate the future value of the initial deposit $A = P (1 + i)^{n}$
  $= 12000 (1 + \frac{0 , 095}{12})^{48}$
  $= R 17521, 17895...$
  1 mark · Use the compound interest formula
4. ✓
  Identify the number of payments for the annuityDeposits start 1 April 2023 and end 1 March 2025.
  From April 2023 to March 2025 inclusive is $24$ months/deposits.
  $n = 24$
  1 mark · Find i and n per period
5. ✓
  Calculate the future value of the annuity $F = \frac{x [( 1 + i ) ^{n} - 1 ]}{i}$
  $= \frac{500 [ ( 1 + \frac{0 , 095}{12} ) ^{24} - 1 ]}{\frac{0 , 095}{12}}$
  $= R 13158, 64744...$
  1 mark · Use the future value formula
6. ✓
  Add the values to find the total amount $Total = 17521, 17895... + 13158, 64744...$
  $= R 30679, 83$
  1 mark · Use the future value formula
4. Question 8.3 · November 2025 · Paper 1 · Provincial · 5 marks
8.3 Rodney starts an investment with a deposit of R25 000. Two years later, he deposits another R10 000. Exactly four years after he started the investment, he withdraws R5 000. For the first two years, the interest is calculated at 4% per annum, compounded monthly and thereafter it is calculated at 7% per annum, compounded semi-annually.

What is the accumulated amount of the investment exactly five years after the initial deposit?(5)
Show the memo (5 ticks)Memo
1. ✓
  $n = 24$ ; $6$ and $2$ $n = 2 \times 12 = 24$ (monthly, years 0–2)
  $n = 3 \times 2 = 6$ (half-yearly, years 2–5)
  $n = 1 \times 2 = 2$ (half-yearly, years 4–5)
  1 mark · Find i and n per period
2. ✓
  $25000 (1 + \frac{4%}{12})^{24}$ $25000 (1 + \frac{4%}{12})^{24}$
  1 mark · Use the compound interest formula
3. ✓
  $+ 10000$ to $25000 (1 + \frac{4%}{12})^{24}$ $(25000 (1 + \frac{4%}{12})^{24} + 10000) (1 + \frac{7%}{2})^{6}$
  1 mark · Use the compound interest formula
4. ✓
  Subtracting 5 000 with its interest $- 5000 (1 + \frac{7%}{2})^{2}$
  1 mark · Use the compound interest formula
5. ✓
  Answer $A =$ R40 222,91
  1 mark · Use the compound interest formula
5. Question 7.3 · May/June 2024 · Paper 1 · National (DBE) · 6 marks
7.3 Lesibana was granted a loan of R225 000. The rate of interest for the loan is 9% p.a., compounded monthly. Lesibana will make monthly payments of R5 500, starting exactly four months after the loan was granted. How many payments will Lesibana make to settle the loan?(6)
Show the memo (6 ticks)Memo
1. ✓
  Monthly interest rate i $i = \frac{0 , 09}{12}$
  1 mark · Find i and n per period
2. ✓
  Substitution into the compound interest (A) formula $225000 (1 + \frac{0 , 09}{12})^{3}$
  1 mark · Use the compound interest formula
3. ✓
  n = 3 in the A-formula (the loan grows for 3 months before the first payment) $n = 3$
  1 mark · Find i and n per period
4. ✓
  Substitution into the present value formula $225000 (1 + \frac{0 , 09}{12})^{3} = \frac{5 500 [ 1 - ( 1 + \frac{0 , 09}{12} ) ^{- n} ]}{\frac{0 , 09}{12}}$
  1 mark · Use the present value formula
5. ✓
  Correct use of logs $(1 + \frac{0 , 09}{12})^{- n} = 0, 6862265041 \dots$
  $- n = lo g_{(1 + \frac{0 , 09}{12})} 0, 6862265041 \dots$
  $n = 50, 39 \dots$
  1 mark · Find an exponent using logs
6. ✓
  Number of payments $n = 51$ payments
  1 mark · Round off to required accuracy
6. Question 1.3 · September 2024 · Provincial · 4 marks
An advertisement in a local newspaper reads as follows:
Buy an iPhone 14 Pro Max cell phone for only R1 029 per month. You have 36 months to pay.
• No deposit is required.
1.3 The cost of the cell phone is subject to inflation and increases to a cash price of R31 968,11 after 3 years. Calculate the annual inflation rate.(4)
Show the memo (4 ticks)Memo
1. ✓
  Formula $A = P (1 + i)^{n}$
  1 mark · Use the compound interest formula
2. ✓
  Substitution $31968, 11 = 29730, 34 (1 + i)^{3}$
  1 mark · Use the compound interest formula
3. ✓
  Make i the subject $i = 3 \frac{31968 , 11}{29730 , 34} - 1$
  1 mark · Solve an equation with rational exponents
4. ✓
  Final answer $i = 2, 45%$
  1 mark · Use the compound interest formula

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