Hire Purchase, Exchange Rates & Population Growth (Grade 10)

Working out a hire-purchase agreement with a deposit and monthly instalments, converting between currencies, and using the compound formula for population growth.

1Hire purchase

Hire purchase is buying on credit: you pay a deposit, then equal monthly instalments on the balance. The interest is charged as simple interest on the balance for the full period.

balance = cash price − deposit
interest = balance × i × n
total owing = balance + interest
monthly instalment = total owingnumber of months

Worked ExampleA fridge costs R12 000. A 10% deposit is paid and the balance is repaid over 3 years at 15% p.a. simple interest. Calculate the monthly instalment.

1
Deposit = 10% of R12 000 = R1 200.
2
Balance = 12 000 − 1 200 = R10 800.
Interest is charged on the balance, NOT the cash price.
3
Interest = 10 800 × 0,15 × 3 = R4 860.
Simple interest over the full 3 years.
4
Total owing = 10 800 + 4 860 = R15 660.
5
Monthly instalment = 15 66036 = R435,00.
3 years = 36 months.

⚠️

Charging the interest on the full R12 000 is the classic error. The deposit is paid immediately, so interest is only charged on what is still owed.

💡

The total actually paid is deposit + total owing = R1 200 + R15 660 = R16 860 — R4 860 more than the cash price. Questions often ask for exactly that comparison.

2Foreign exchange rates

An exchange rate tells you how many rand one unit of another currency costs. If the rate is R18,50 to the dollar, then $1 = R18,50.

Worked ExampleA camera costs $240 in the USA. The exchange rate is R18,50 to the dollar. What does it cost in rand?

1
240 × 18,50.
Dollars → rand: multiply by the rate.
2
= R4 440.

Worked ExampleA tourist changes R9 250 into dollars at R18,50 to the dollar. How many dollars does she get?

1
9 25018,50.
Rand → dollars: divide by the rate.
2
= $500.

💡

Sanity-check the direction: a rand is worth much less than a dollar, so a rand amount must give a smaller number of dollars. If your answer got bigger, you divided when you should have multiplied.

A weakening rand (rate rises from R18,50 to R19,50) makes imports, petrol and overseas travel more expensive, but makes South African exports cheaper for foreign buyers.

3Population growth

A = P(1 + i)ⁿ

Population grows compound, because each year's growth is calculated on the new, larger population.

Worked ExampleA town of 1 200 000 people grows at 1,8% per year. Estimate the population after 5 years.

1
A = 1 200 000(1 + 0,018)⁵.
i = 1,8% = 0,018.
2
= 1 200 000(1,018)⁵.
3
≈ 1 311 959 people.
Round to a whole number — you cannot have part of a person.

Practice exercises

Work each one out, then click to reveal the answer.

📄 Worksheet ✅ Memo 📝 Exam paper 🗝️ Marking guide

1
A fridge costs R12 000. A 10% deposit is paid. Calculate the deposit and the balance owing.
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Deposit = R1 200; balance = R10 800
2
The R10 800 balance is repaid over 3 years at 15% p.a. simple interest. Calculate the interest.
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10 800 × 0,15 × 3 = R4 860
3
Calculate the monthly instalment for that hire-purchase agreement.
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15 66036 = R435,00
4
How much more than the cash price does the buyer pay in total?
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R1 200 + R15 660 = R16 860, which is R4 860 more
5
A camera costs $240. The rate is R18,50 to the dollar. Calculate the cost in rand.
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240 × 18,50 = R4 440
6
A tourist changes R9 250 into dollars at R18,50 to the dollar. How many dollars does she receive?
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9 25018,50 = $500
7
A town of 1 200 000 grows at 1,8% p.a. Estimate the population after 5 years.
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1 200 000(1,018)⁵ ≈ 1 311 959
8
Explain the effect on the petrol price when the rand weakens against the dollar.
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Oil is bought in dollars, so a weaker rand means more rand are needed per dollar and the petrol price rises.