Grade 12 Maths · Financial Maths · Handle late, missed or changed payments

Handle late, missed or changed payments Grade 12

Draw a timeline for a loan or savings plan where the first payment starts later, some payments are missed, or the payment or interest rate changes part way, then move each amount to the right time to find the answer.

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Financial Mathematics Grade 12: L7 Deferred AnnuitiesOnline Maths by Miss Pythagoras

Grade 12 Financial Maths loan repayments with MISSED PAYMENTS examples from Past Exam Papers| NTENTE \ New Technological Education

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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)

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

More past paper questions: handle late, missed or changed payments

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3. Question 6.3.2 · November 2022 · Paper 1 · National (DBE) · 5 marks
6.3 Thabo plans to buy a car that costs R250 000. He will pay a deposit of $15%$ and take out a loan for the balance. The interest on the loan is $13%$ p.a., compounded monthly.

Answer the following.
6.3.2 The first repayment will be made 6 months after the loan has been granted. The loan will be repaid over a period of 6 years after it has been granted. Calculate the MONTHLY instalment.(5)
Show the memo (5 ticks)Memo
1. ✓
  $A = 212500 (1 + \frac{0 , 13}{12})^{5}$ $A = 212500 (1 + \frac{0 , 13}{12})^{5}$
  1 mark · Handle late, missed or changed payments
2. ✓
  Answer $A = 224262, 53$
  1 mark · Use the compound interest formula
3. ✓
  Substitution into correct formula $P = \frac{x [ 1 - ( 1 + i ) ^{- n} ]}{i}$
  $224262, 53 = \frac{x [ 1 - ( 1 + \frac{0 , 13}{12} ) ^{- 67} ]}{\frac{0 , 13}{12}}$
  1 mark · Use the present value formula
4. ✓
  $- 67$ $n = 67$
  1 mark · Handle late, missed or changed payments
5. ✓
  Answer $∴ x =$ R4 724,96
  1 mark · Use the present value formula
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 · Handle late, missed or changed payments
2. ✓
  Correct i and n $i = \frac{0 , 095}{12}; n = 5$
  1 mark · Handle late, missed or changed payments
3. ✓
  Answer $R 10402, 15$
  1 mark · Use the compound interest formula
5. Question 6.2.1 · September 2024 · Paper 1 · Provincial · 3 marks
6.2 A loan of R300 000 is taken out at an interest rate of $5, 3%$ p.a. compounded quarterly. The loan was taken out on the 1st of March 2016. The first payment was made on 1 December 2016 and is repaid in $72$ equal quarterly payments.

Answer the questions that follow.
6.2.1 What is the outstanding balance of the loan on 1 September 2016?(3)
Show the memo (3 ticks)Memo
1. ✓
  $4$ and $2$ $i = \frac{0 , 053}{4}$ and $n = 2$
  1 mark · Handle late, missed or changed payments
2. ✓
  Correct substitution in correct formula $A = 300000 (1 + \frac{0 , 053}{4})^{2}$
  1 mark · Handle late, missed or changed payments
3. ✓
  Answer $A =$ R308 002,67
  1 mark · Use the compound interest formula
6. Question 6.3.1 · September 2026 · Paper 1 · Provincial · 4 marks
6.3 Kim takes out a loan of R750 000 to buy a house. She plans to repay the loan over 20 years after the loan is granted by means of equal monthly instalments. The interest rate is 11,5% p.a. compounded monthly.

Answer the questions that follow.
6.3.1 Calculate her monthly repayments, if the first payment starts six months after the loan was drawn.(4)
Show the memo (4 ticks)Memo
1. ✓
  $n = 235$ $n = 240 - 5 = 235$
  1 mark · Handle late, missed or changed payments
2. ✓
  Loan grown for 5 months $750000 (1 + \frac{11 , 5%}{12})^{5}$
  1 mark · Handle late, missed or changed payments
3. ✓
  Substitution $P_{v} = \frac{x [ 1 - ( 1 + i ) ^{- n} ]}{i}$
  $750000 (1 + \frac{11 , 5%}{12})^{5} = \frac{x [ 1 - ( 1 + \frac{11 , 5%}{12} ) ^{- 235} ]}{\frac{11 , 5%}{12}}$
  1 mark · Use the present value formula
4. ✓
  Answer $x = \frac{750 000 ( 1 + \frac{11 , 5%}{12} ) ^{5} ( \frac{11 , 5%}{12} )}{[ 1 - ( 1 + \frac{11 , 5%}{12} ) ^{- 235} ]}$
  $x =$ R8 435,36
  1 mark · Use the present value formula

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