Grade 12 Maths · Financial Maths · Paper 1

Annuities (Future and Present Value) Grade 12

Real Annuities (Future and Present Value) past paper questions and answers from 2024 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 7.2 · May/June 2025 · Paper 1 · National (DBE) · 5 marks

7.2 Tino invests

R 500000

in an account earning interest at the rate of

6%

p.a., compounded quarterly. Tino decides to withdraw

R 11250

at the end of every

3

months. Tino will continue making these regular withdrawals until there is no money in the account. How many withdrawals of

R 11250

will Tino be able to make?(5)

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

Annuities (Future and Present Value) skills

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More Annuities (Future and Present Value) Grade 12 questions and answers

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4. Question 7.2.1 · September 2024 · Paper 1 · Provincial · 3 marks
7.2 Micaela buys furniture to the value of R10 000. She borrows the money on 1 February 2023 from a financial institution that charges interest at a rate of 9,5% p.a. compounded monthly. Micaela agrees to pay monthly instalments of R450. The loan agreement allows Micaela to start paying equal monthly instalments from 01 August 2023.
7.2.1 Calculate the total amount owing to the financial institution on 1 July 2023.(3)
Show the memo (3 ticks)Memo
1. ✓
  Substitute into correct formula $A = 10000 (1 + \frac{0 , 095}{12})^{5}$
  1 mark · Use the compound interest formula
2. ✓
  Correct i and n $i = \frac{0 , 095}{12}; n = 5$
  1 mark · Find i and n per period
3. ✓
  Answer $R 10402, 15$
  1 mark · Use the compound interest formula
5. Question a · Siyavula Grade 12 Mathematics, 3.3 Future value annuities, Worked example 4 · 3 marks
Ciza decides to start saving money for the future. At the end of each month she deposits R900 into an account at Harringstone Mutual Bank, which earns $8, 25%$ interest p.a. compounded monthly.
a Determine the balance of Ciza's account after $29$ years.(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula and values $F = \frac{x [ ( 1 + i ) ^{n} - 1 ]}{i}$
  $x = 900$ ; $i = \frac{0 , 0825}{12}$ ; $n = 29 \times 12 = 348$
  1 mark · Use the future value formula
2. ✓
  Substitution $F = \frac{900 [ ( 1 + \frac{0 , 0825}{12} ) ^{348} - 1 ]}{\frac{0 , 0825}{12}}$
  1 mark · Use the future value formula
3. ✓
  Answer $F = R 1289665, 06$
  1 mark · Use the future value formula
6. Question WE5 · Siyavula Grade 12 Mathematics, 3.3 Future value annuities, Worked example 5 · 3 marks
WE5 Kosma is planning a trip to Canada to visit her friend in two years' time. She makes an itinerary for her holiday and she expects that the trip will cost R25 000. How much must she save at the end of every month if her savings account earns an interest rate of $10, 7%$ per annum compounded monthly?(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula and values $F = \frac{x [ ( 1 + i ) ^{n} - 1 ]}{i}$ , so $x = \frac{F \times i}{[ ( 1 + i ) ^{n} - 1 ]}$
  $F = 25000$ ; $i = \frac{0 , 107}{12}$ ; $n = 2 \times 12 = 24$
  1 mark · Use the future value formula
2. ✓
  Substitution $x = \frac{25 000 \times \frac{0 , 107}{12}}{[ ( 1 + \frac{0 , 107}{12} ) ^{24} - 1 ]}$
  1 mark · Use the future value formula
3. ✓
  Answer $x = R 938, 80$
  Kosma must save R938,80 each month so that she can afford her holiday.
  1 mark · Use the future value formula
7. Question WE6 · Siyavula Grade 12 Mathematics, 3.3 Future value annuities, Worked example 6 · 3 marks
WE6 Simon starts to save for his retirement. He opens an investment account and immediately deposits R800 into the account, which earns $12, 5%$ per annum compounded monthly. Thereafter, he deposits R800 at the end of each month for $20$ years. What is the value of his retirement savings at the end of the $20$ year period?(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula and values $F = \frac{x [ ( 1 + i ) ^{n} - 1 ]}{i}$
  $x = 800$ ; $i = \frac{0 , 125}{12}$ ; $n = 1 + (20 \times 12) = 241$
  1 mark · Use the future value formula
2. ✓
  Substitution $F = \frac{800 [ ( 1 + \frac{0 , 125}{12} ) ^{241} - 1 ]}{\frac{0 , 125}{12}}$
  1 mark · Use the future value formula
3. ✓
  Answer $F = R 856415, 66$
  Simon will have saved R856 415,66 for his retirement.
  1 mark · Use the future value formula
8. Question b · Siyavula Grade 12 Mathematics, 3.3 Future value annuities, Worked example 7 · 3 marks
Wellington Courier Company buys a delivery truck for R296 000. The value of the truck depreciates on a reducing-balance basis at $18%$ per annum. The company plans to replace this truck in seven years' time and they expect the price of a new truck to increase annually by $9%$ .
b Determine the minimum balance of the sinking fund in order for the company to afford a new truck in seven years' time.(3)
Show the memo (3 ticks)Memo
1. ✓
  Substitution $P = 296000$ ; $i = 0, 09$ ; $n = 7$
  $A = P (1 + i)^{n} = 296000 (1 + 0, 09)^{7}$
  1 mark · Use the compound interest formula
2. ✓
  Price of new truck $A = R 541099, 58$
  1 mark · Use the compound interest formula
3. ✓
  Sinking fund $F = R 541099, 58 - R 73788, 50 = R 467311, 08$
  1 mark · Use the future value formula
9. Question a · Siyavula Grade 12 Mathematics, 3.4 Present value annuities, Worked example 10 · 4 marks
For calculations, assume the prime lending rate is $8, 5%$ per annum.
A school sells its old bus and uses the proceeds as a $15%$ deposit for the purchase of the new bus, which costs R330 000. To finance the balance of the purchase, the school takes out a loan that is subject to an interest rate of prime $+ 1%$ compounded monthly. The repayment period of the loan is $3$ years.
a Calculate the monthly repayments.(4)
Show the memo (4 ticks)Memo
1. ✓
  Loan amount $P = R 330000 - (\frac{15}{100} \times R 330000) = R 330000 - R 49500 = R 280500$
  1 mark · Calculate with percentages
2. ✓
  Formula and values $x = \frac{P \times i}{[ 1 - ( 1 + i ) ^{- n} ]}$
  $i = \frac{0 , 095}{12}$ (prime $8, 5% + 1% = 9, 5%$ ); $n = 3 \times 12 = 36$
  1 mark · Use the present value formula
3. ✓
  Substitution $x = \frac{280 500 \times \frac{0 , 095}{12}}{[ 1 - ( 1 + \frac{0 , 095}{12} ) ^{- 36} ]}$
  1 mark · Use the present value formula
4. ✓
  Answer $x = R 8985, 24$
  The school must pay R8 985,24 per month.
  1 mark · Use the present value formula

Annuities (Future and Present Value) Grade 12 videos

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