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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 3, Complex Procedures
6.1 Two friends, Kuda and Thabo, each want to invest R5 000 for four years. Kuda invests his money in an account that pays simple interest at 8,3% per annum. At the end of four years, he will receive a bonus of exactly 4% of the accumulated amount. Thabo invests his money in an account that pays interest at 8,1% p.a., compounded monthly. Whose investment will yield a better return at the end of four years? Justify your answer with appropriate calculations.

Source: DBE Mathematics Paper 1, November 2019, Question 6.1

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 2, Routine Procedures
Selby wants to save money by making quarterly deposits of R15 000 into a savings account. The account pays interest at a rate of 8,8% per annum, compounded quarterly. He starts making deposits at the end of the first quarter and makes his last deposit at the end of the 16th quarter. 7.1.1 Calculate the total amount in the savings account at the end of the 16th quarter.

Source: DBE Mathematics Paper 1, November 2018, Question 7.1.1

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
6.2 Nine years ago, a bank granted Mandy a home loan of R525 000. This loan was to be repaid over 20 years at an interest rate of 10% p.a., compounded monthly. Mandy's monthly repayments commenced exactly one month after the loan was granted. 6.2.1 Mandy decided to make monthly repayments of R6 000 instead of the required R5 066,36. How many payments will she make to settle the loan?

Source: DBE Mathematics Paper 1, November 2019, Question 6.2.1

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.