Grade 12 Maths · Financial Maths

Calculate the outstanding loan balance

Find how much is still owed on a loan after some payments, for example the amount left on a car loan after 3 years.

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Outstanding balance grade 12: Present value methodKevinmathscience

Outstanding balance grade 12: Future value methodKevinmathscience

Grade 12 Financial Maths Lesson 7 | Calculating the Balance of a Loan | Mlungisi NkosiMlungisi Nkosi Maths & Science

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Question 8.4 · November 2025 · Paper 1 · Provincial · 6 marks

8.4 Brian borrows R

x

at an annual interest rate of 12% p.a. He has two options to repay the loan.

OPTION 1: Pay R5 000, 2 years after the loan was granted and the remaining amount, 4 years after the loan was granted. The interest is compounded annually.

OPTION 2: Pay R3 000, 1 year after the loan was granted and the remaining amount, 3 years after the loan was granted. The interest is compounded semi-annually.

If the final payments (the remaining amounts) in both options are the same, calculate the value of

x

.(6)

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

More past paper questions: calculate the outstanding loan balance

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3. Question 7.2.3 · 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.
7.2.3 What is the balance of the loan immediately after Micaela has made the $2 5^{t h}$ payment?(3)
Show the memo (3 ticks)Memo
1. ✓
  Loan accumulated to the 25th payment $10402, 15 (1, 0079)^{25}$
  1 mark · Calculate the outstanding loan balance
2. ✓
  Payments accumulated $\frac{450 [( 1 , 0079 ) ^{25} - 1 ]}{0 , 0079}$
  1 mark · Calculate the outstanding loan balance
3. ✓
  Answer $R 282, 36$
  1 mark · Calculate the outstanding loan balance
4. Question 7.3.2 · November 2024 · Paper 1 · National (DBE) · 7 marks
7.3 Tshepo was granted a loan of R100 000 on 1 March 2022 at an interest rate of 13,5% p.a., compounded monthly. Tshepo agreed to repay the loan over 5 years in monthly instalments of R2 300,98, starting on 1 April 2022.
7.3.2 Tshepo paid R22 300,98 (his monthly instalment and an additional R20 000) on 1 March 2024 into the loan account. He continues to pay the original monthly instalment thereafter. How many months earlier will Tshepo repay the loan?(7)
Show the memo (6 ticks)Memo
1. ✓
  Calculate Balance after 2 years (24 months) $P = \frac{x [ 1 - ( 1 + i ) ^{- n} ]}{i}$
  Remaining period $n = 60 - 24 = 36$
  Balance $= \frac{2300 , 98 [ 1 - ( 1 + \frac{13 , 5}{1200} ) ^{- 36} ]}{\frac{13 , 5}{1200}}$
  2 marks · Calculate the outstanding loan balance
2. ✓
  Determine outstanding balance valueBalance $= R 67804, 94$
  1 mark · Calculate the outstanding loan balance
3. ✓
  Adjust balance for lump sum paymentNew Balance $= 67804, 94 - 20000 = R 47804, 94$
  1 mark · Calculate the outstanding loan balance
4. ✓
  Calculate new repayment period $47804, 94 = \frac{2300 , 98 [ 1 - ( 1 + \frac{13 , 5}{1200} ) ^{- n} ]}{\frac{13 , 5}{1200}}$
  $0, 766... = (1, 01125)^{- n}$
  1 mark · Use the present value formula
5. ✓
  Solve for n using logs $- n = lo g_{1, 01125} (0, 766...)$
  $n = 23, 83$
  1 mark · Find an exponent using logs
6. ✓
  Calculate time savedOriginal remaining: 36 months
  Time saved $= 36 - 23, 83 \approx 12, 17$
  Answer: 12 months earlier
  1 mark · Find an exponent using logs

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