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Grade 12 Finance Growth Decay — How to Identify the Question Type

Grade 12 finance builds on Grade 11 by adding future value annuities, present value annuities, and loan/bond calculations. Identify whether money is being paid IN (future value annuity) or paid OUT (present value annuity) before choosing a formula.

Type 1: Compound interest and decay (revision foundation)

Trigger words: "Compound interest", "depreciated on a reducing balance", "A ="

Trigger structure: A lump sum grows or depreciates — no regular payments. This is the Grade 11 formula still used as a foundation for Grade 12 multi-phase problems.

Method (no numbers — just the steps)

  1. Growth: A = P(1 + i)^n
  2. Decay (reducing balance): A = P(1 − i)^n
  3. Convert annual rate to period rate if compounding is monthly/quarterly: i_period = i_annual/m
  4. Adjust n to match the compounding period
Grade 12Paper 1Level 2 — Routine Procedures
5.1 R50 000 is invested at 9% per annum compounded monthly for 5 years. Calculate the accumulated amount.

Source: DBE Mathematics Paper 1, November 2022, Question 5.1

See the progression — same type, increasing difficulty

Easy
R20 000 is invested at 8% p.a. compounded annually for 4 years. Calculate A.

Practice question — not sourced from a past paper.

Medium
A car worth R300 000 depreciates at 15% p.a. on a reducing balance. Find its value after 5 years.

Practice question — not sourced from a past paper.

Hard
R10 000 is invested at 12% p.a. compounded quarterly. After how many years will the investment double?

Practice question — not sourced from a past paper.

Type 2: Future value annuity

Trigger words: "Regular deposits", "saving plan", "how much will be in the account", "Fv ="

Trigger structure: Equal payments are made at regular intervals INTO an account. You are asked for the total amount accumulated at the end.

Do not confuse with: Present value annuity — in a future value annuity money goes IN; in a present value annuity money comes OUT (loan repayments).

Method (no numbers — just the steps)

  1. Use: Fv = x[(1 + i)^n − 1]/i
  2. x = payment amount per period
  3. i = interest rate per period (annual rate ÷ number of periods per year)
  4. n = total number of payments
Grade 12Paper 1Level 3 — Complex Procedures
5.2 R2 000 is deposited at the end of each month into an account earning 7,2% p.a. compounded monthly. Calculate the value of the account after 3 years.

Source: DBE Mathematics Paper 1, November 2023, Question 5.2

Common mistake

Using the annual interest rate directly when payments are monthly — always divide the rate by 12 and multiply n by 12.

See the progression — same type, increasing difficulty

Easy
R500 is deposited at the end of each month for 2 years at 6% p.a. compounded monthly. Find the future value.

Practice question — not sourced from a past paper.

Medium
A learner wants to save R100 000 in 5 years. The account pays 8,4% p.a. compounded monthly. How much must be deposited monthly?

Practice question — not sourced from a past paper.

Hard
R1 000 is deposited at the END of each month for 3 years into an account at 9% p.a. compounded monthly. Immediately after the last deposit, the interest rate changes to 10,8% p.a. compounded monthly. Calculate the value of the investment 2 years after the rate change.

Practice question — not sourced from a past paper.

Type 3: Present value annuity (loan repayments)

Trigger words: "Monthly repayments", "loan", "bond", "how much is still owed", "Pv ="

Trigger structure: A lump sum is borrowed NOW and repaid in equal instalments. You may be asked for the repayment amount, the outstanding balance, or the total interest paid.

Do not confuse with: Future value annuity — here money is being paid OUT to repay a loan, not saved up.

Method (no numbers — just the steps)

  1. Use: Pv = x[1 − (1 + i)^(−n)]/i
  2. Outstanding balance after k payments: treat remaining payments as a new present value annuity
  3. Total interest paid = (total payments made) − (original loan amount)
Grade 12Paper 1Level 3 — Complex Procedures
5.3 A bank grants a home loan of R800 000 at 9% p.a. compounded monthly, repayable over 20 years. Calculate the monthly repayment.

Source: DBE Mathematics Paper 1, November 2021, Question 5.3

Common mistake

Calculating the outstanding balance using the original loan amount minus payments made — instead, the balance is the present value of all remaining payments.

See the progression — same type, increasing difficulty

Easy
A loan of R50 000 is repaid over 3 years at 12% p.a. compounded monthly. Find the monthly repayment.

Practice question — not sourced from a past paper.

Medium
A car loan of R200 000 is repaid in monthly instalments of R4 500 at 10,8% p.a. compounded monthly. After 3 years, what is the outstanding balance?

Practice question — not sourced from a past paper.

Hard
A bond of R1 200 000 is repaid over 20 years at 9,6% p.a. compounded monthly. After 10 years, the interest rate drops to 8,4% p.a. Calculate the new monthly repayment for the remaining term.

Practice question — not sourced from a past paper.

Words like determine and hence appear throughout this topic — see the instruction word glossary for full definitions.