Grade 11 Maths · Financial Maths · Use a timeline with several payments

Use a timeline with several payments Grade 11

Draw a timeline and move every deposit and withdrawal to the same date, changing the rate where it changes, to find a final amount or an unknown deposit.

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Financial Maths Grade 11 | TimelineKevinmathscience

5. Grade 11 Mathematics - Financial Maths - Timelines: Changing Interest RatesJuniorTukkie at the University of Pretoria

Grade 11 Financial Math: Deposits and Withdrawals (TIMELINE 1)Living The Dream Academy

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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)

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

More questions: use a timeline with several payments

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3. Question 8.3.1 · November 2023 · Paper 1 · Provincial · 5 marks
8.3 Lwandi made an initial deposit of R23 000 into an investment account that paid an interest rate of $9, 25%$ compounded quarterly. After 3 years since the start of his investment, he deposited R13 500 and the interest rate changed to $8, 2%$ p.a. compounded monthly.

Answer the questions that follow.
8.3.1 Calculate the total value of the investment in Lwandi's account at the end of the 5th year.(5)
Show the memo (5 ticks)Memo
1. ✓
  $i$ and $n$ for the first 3 years $i = \frac{0 , 0925}{4}$ and $n = 12$
  1 mark · Find i and n per period
2. ✓
  $i$ and $n$ for the last 2 years $i = \frac{0 , 082}{12}$ and $n = 24$
  1 mark · Find i and n per period
3. ✓
  Value after 3 years plus deposit $(23000 (1 + \frac{0 , 0925}{4})^{12} + 13500)$
  1 mark · Use a timeline with several payments
4. ✓
  Growth for the last 2 years $\times (1 + \frac{0 , 082}{12})^{24}$
  1 mark · Use a timeline with several payments
5. ✓
  Answer $A =$ R51 530,18
  1 mark · Use the compound interest formula
4. Practice · Siyavula Grade 11 Maths · Ex 9.5 · 5 marks
$R 75000$ is invested in an account which offers interest at $11%$ p.a. compounded monthly for the first $24$ months. Then the interest rate changes to $7, 7%$ p.a. compounded half-yearly. If $R 9000$ is withdrawn from the account after one year and then a deposit of $R 3000$ is made three years after the initial investment, how much will be in the account at the end of $6$ years?(5)
Show the memo (5 ticks)Memo
1. ✓
  Timeline $T_{0}$ to $T_{2}$ : $i = \frac{0 , 11}{12}$ ; $T_{2}$ to $T_{6}$ : $i = \frac{0 , 077}{2}$ . Withdrawal at $T_{1}$ , deposit at $T_{3}$ .
  1 mark · Find i and n per period
2. ✓
  Grow the investment $75000 (1 + \frac{0 , 11}{12})^{24} (1, 0385)^{8}$
  1 mark · Use the compound interest formula
3. ✓
  Grow the withdrawal $- 9000 (1 + \frac{0 , 11}{12})^{12} (1, 0385)^{8}$
  1 mark · Use a timeline with several payments
4. ✓
  Grow the deposit $+ 3000 (1, 0385)^{6}$
  1 mark · Use a timeline with several payments
5. ✓
  Balance $A = R 116484, 21$
  1 mark · Use a timeline with several payments
Question adapted from Siyavula Education (CC BY 3.0) · Solution by NavyBlue
5. Practice · Siyavula Grade 11 Maths · Ex 9.7 · 4 marks
$R 145000$ is invested in an account which offers interest at $9%$ p.a. compounded half-yearly for the first $2$ years. Then the interest rate changes to $4%$ p.a. compounded quarterly. Four years after the initial investment, $R 20000$ is withdrawn. $6$ years after the initial investment, a deposit of $R 15000$ is made. Determine the balance of the account at the end of $8$ years.(4)
Show the memo (4 ticks)Memo
1. ✓
  Timeline $T_{0}$ to $T_{2}$ : $i = 0, 045$ per half-year; $T_{2}$ to $T_{8}$ : $i = 0, 01$ per quarter. Withdrawal at $T_{4}$ , deposit at $T_{6}$ .
  1 mark · Find i and n per period
2. ✓
  Grow the investment $145000 (1, 045)^{4} (1, 01)^{24}$
  1 mark · Use the compound interest formula
3. ✓
  Withdrawal and deposit $- 20000 (1, 01)^{16} + 15000 (1, 01)^{8}$
  1 mark · Use a timeline with several payments
4. ✓
  Balance $A = R 212347, 69$
  1 mark · Use a timeline with several payments
Question adapted from Siyavula Education (CC BY 3.0) · Solution by NavyBlue
6. Practice · Siyavula Grade 11 Maths · Ex 9.7 · 3 marks
Tintin invests $R 120000$ . He is quoted a nominal interest rate of $7, 2%$ per annum compounded monthly.
(c) Suppose Tintin invests his money for a total period of $4$ years, but after $18$ months makes a withdrawal of $R 20000$ , how much will he receive at the end of the $4$ years?(3)
Show the memo (3 ticks)Memo
1. ✓
  Grow the investment $120000 (1, 0744)^{4}$
  1 mark · Use the compound interest formula
2. ✓
  Grow the withdrawal $- 20000 (1, 0744)^{2, 5}$
  1 mark · Use a timeline with several payments
3. ✓
  Amount $A = R 135968, 69$
  1 mark · Use the compound interest formula
Question adapted from Siyavula Education (CC BY 3.0) · Solution by NavyBlue

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