Grade 10 Finance and Growth

Grade 10 finance and growth: simple and compound interest, hire purchase, inflation, population growth and exchange rates, with worked CAPS examples.

Finance and growth is about 10 marks of Grade 10 Paper 1, and it is the most practical topic in the syllabus. You use two formulas: simple interest A = P(1 + in) and compound interest A = P(1 + i)ⁿ. With them you calculate investments, hire purchase agreements, inflation and population growth, and you convert between currencies using exchange rates.

Grade 11 adds depreciation, nominal and effective interest rates and timelines, and Grade 12 adds annuities, so being fluent with these two formulas now is the foundation of all later finance work.

Key concepts

  • Simple interest: A = P(1 + in)
  • Compound interest: A = P(1 + i)ⁿ
  • Hire purchase: simple interest on the amount owed after the deposit
  • Inflation and population growth use the compound growth formula
  • Exchange rates: converting currencies with a given rate
  • i is the rate as a decimal; n is the number of years

Worked examples

R8 000 is invested at 9% p.a. compounded annually for 4 years. Find the final amount.

A = P(1 + i)ⁿ = 8 000(1.09)⁴ = R11 292.65. With simple interest it would only be 8 000(1 + 0.09 × 4) = R10 880.

A TV costs R6 000. You pay a 10% deposit and the balance over 2 years at 15% p.a. simple interest. Find the monthly instalment.

Deposit = R600, so R5 400 is owed. A = 5 400(1 + 0.15 × 2) = R7 020. Monthly instalment = 7 020 ÷ 24 = R292.50.

A loaf of bread costs R20 today. With inflation at 6% p.a., what will it cost in 2 years?

Inflation compounds: A = 20(1.06)² = R22.47.

The exchange rate is $1 = R18.20. How many US dollars do you get for R5 000?

Divide the rand amount by the rate: 5 000 ÷ 18.20 = 274.725…, so you get $274.73. To convert dollars back to rand, multiply by the rate instead.

Common mistakes

  • Using 9 instead of 0.09 for i.
  • Charging hire purchase interest on the full price instead of the amount after the deposit.
  • Rounding in the middle of a calculation instead of only at the end.
  • Using the simple interest formula when the question says compounded.

Exam tips

  • Write down P, i and n before you substitute.
  • Keep the full calculator value until the final answer, then round to the nearest cent.
  • Read for the word 'compounded'; without it, the question usually means simple interest.

Frequently asked questions

What is the difference between simple and compound interest?

Simple interest is calculated on the original amount only. Compound interest is calculated on the original amount plus the interest already earned, so it grows faster.

How is hire purchase calculated in Grade 10?

Subtract the deposit, add simple interest on the balance for the term, then divide by the number of months to get the instalment.

Are annuities in Grade 10?

No. Future and present value annuities are Grade 12 work.

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