Grade 12 Maths · Financial Maths · Plan a sinking fund

Plan a sinking fund Grade 12

Work out the scrap value of old equipment (depreciation) and the cost of new equipment (inflation), find the shortfall, then calculate the monthly payment into a fund that will cover it.

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Sinking Fund Gr 12 Financial MathsKevinmathscience

Grade 12 Financial Maths Lesson 6| Sinking Funds | The cost of Replacing Equipment through AnnuitiesMlungisi Nkosi Maths & Science

Financial Mathematics Grade 12: L6 Sinking FundsOnline Maths by Miss Pythagoras

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Practice · Siyavula Grade 12 Maths · Ex 3.3 · 2 marks

Atlantic Transport Company buys a van for

R 265000

. The value of the van depreciates on a reducing-balance basis at

17%

per annum. The company plans to replace this van in five years' time and they expect the price of a new van to increase annually by

12%

11%

per annum compounded monthly.(2)

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

More past paper questions: plan a sinking fund

Work each one out first, then open the memo and check every tick.

3. Question 7.2.3 · May/June 2022 · Paper 1 · National (DBE) · 5 marks
7.2 A company purchased machinery for R500 000. After $5$ years, the machinery was sold for R180 000 and new machinery was bought.

Answer the following.
7.2.3 The company set up a sinking fund and made the first payment into this fund on the day the old machinery was bought. The last payment was made three months before the new machinery was purchased at the end of the 5 years. The interest earned on the sinking fund was $10, 25%$ p.a., compounded monthly. The money from the sinking fund and the R180 000 from the sale of the old machinery was used to pay for the new machinery.

Calculate the monthly payment into the sinking fund.(5)
Show the memo (5 ticks)Memo
1. ✓
  Value of sinking fundSinking fund $= 678635, 11 - 180000$
  $= R 498635, 11$
  1 mark · Plan a sinking fund
2. ✓
  $\frac{0 , 1025}{12}$ $i = \frac{0 , 1025}{12}$
  1 mark · Find i and n per period
3. ✓
  $n = 58$ $n = 58$
  1 mark · Find i and n per period
4. ✓
  $(1 + \frac{0 , 1025}{12})^{3}$ $498635, 11 = \frac{x [ ( 1 + \frac{0 , 1025}{12} ) ^{58} - 1 ]}{\frac{0 , 1025}{12}} (1 + \frac{0 , 1025}{12})^{3}$
  1 mark · Use the compound interest formula
5. ✓
  Answer $x = R 6510, 36$
  1 mark · Plan a sinking fund
4. Question 6.2.2 · November 2023 · Paper 1 · National (DBE) · 4 marks
6.2 Kuda bought a laptop for R10 000 on 31 January 2019. He will replace it with a new one in 5 years' time on 31 January 2024.

Answer the questions that follow.
6.2.2 Kuda will buy a laptop that costs R20 000. In order to cover the cost price, he made his first monthly deposit into a savings account on 28 February 2019. He will make his 60th monthly deposit on 31 January 2024. The savings account pays interest at 8,7% p.a., compounded monthly. Calculate Kuda's monthly deposit into this account.(4)
Show the memo (4 ticks)Memo
1. ✓
  $i$ $i = \frac{8 , 7}{1200}$
  1 mark · Find i and n per period
2. ✓
  $n$ $n = 60$
  1 mark · Find i and n per period
3. ✓
  Substitution into correct formula $F = \frac{x [( 1 + i ) ^{n} - 1 ]}{i}$
  $20000 = \frac{x [ ( 1 + \frac{8 , 7}{1200} ) ^{60} - 1 ]}{\frac{8 , 7}{1200}}$
  1 mark · Use the future value formula
4. ✓
  Answer $x =$ R267,26
  1 mark · Plan a sinking fund
5. Question 7.1.3 · September 2025 · Paper 1 · Provincial · 3 marks
7.1 A business buys a machine that costs R120 000.

Answer the questions that follow.
7.1.3 The business estimates that it will need approximately R90 000 by the end of 5 years. A sinking fund for approximately R90 000, into which equal monthly instalments must be paid, is set up. Interest on this fund is 8,5% per annum, compounded monthly. The first payment will be made immediately and the last payment will be made at the end of the 5-year period.
Calculate the value of the monthly payments into the sinking fund.(3)
Show the memo (3 ticks)Memo
1. ✓
  Value of $i$ and $n$ $i = \frac{0 , 085}{12}$ and $n = 61$
  1 mark · Find i and n per period
2. ✓
  Substitute correctly into the correct formula $F_{v} = \frac{x [( 1 + i ) ^{n} - 1 ]}{i}$
  $90000 = \frac{x [ ( 1 + \frac{0 , 085}{12} ) ^{61} - 1 ]}{\frac{0 , 085}{12}}$
  1 mark · Plan a sinking fund
3. ✓
  Answer $∴ x =$ R1 184,68
  1 mark · Plan a sinking fund
6. Question 6.2.3 · September 2026 · Paper 1 · Provincial · 4 marks
6.2 After 5 years, both assets in 6.1 (K and T) are traded in for new machinery of a value of R70 000. A sinking fund is set-up at the time the two assets are bought for the balance of a new machine.

Answer the questions that follow.
6.2.3 If the sinking fund is set-up at 11% p.a. compounded monthly for 5 years, calculate the value of the regular payments.(4)
Show the memo (4 ticks)Memo
1. ✓
  Substitution into $F$ $R 28750 = \frac{x [ ( 1 + \frac{0 , 11}{12} ) ^{5 \times 12} - 1 ]}{\frac{0 , 11}{12}}$
  1 mark · Plan a sinking fund
2. ✓
  $i = \frac{0 , 11}{12}$ $i = \frac{0 , 11}{12}$
  1 mark · Find i and n per period
3. ✓
  $n = 60$ $n = 60$
  1 mark · Find i and n per period
4. ✓
  Answer $x = R 361, 55$
  1 mark · Plan a sinking fund

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