Simple Interest & Budgets (Grade 8)

Working out simple interest on savings and loans, finding the total amount owed or saved, and drawing up a monthly budget that balances.

1Simple interest

Interest is the rent you pay for using money — the bank pays you when you save, and you pay the bank when you borrow. With simple interest it is worked out on the original amount every year.

I = P × i × n

P = the original amount · i = the rate as a decimal · n = number of years

Total amount: A = P + I

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Turn the percentage into a decimal first: 7,5% → 7,5 ÷ 100 = 0,075. Forgetting this is the single most common error.

Worked ExampleR4 000 is invested at 7,5% simple interest per year for 3 years. Calculate the interest and the total.

1
P = 4 000, i = 0,075, n = 3.
Write down what you have before substituting.
2
I = 4 000 × 0,075 × 3.
3
= R900.
That is R300 of interest each year, for three years.
4
A = 4 000 + 900 = R4900.
The total in the account after 3 years.

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I is the interest only, not the total. If a question asks 'how much is in the account', you must still add P.

2Budgets

A budget is a plan for your money: what comes in, and where it all goes. A budget balances when the two sides are equal.

A monthly budget on an income of R6500. The six amounts add to exactly R6500, so this budget balances.

Worked ExampleFrom the budget above, what percentage of the income goes on rent?

1
Rent is R2 200 out of R6500.
2
2 2006500 × 100.
Part over whole, times 100.
3
= 33,8%.
Just over a third of the income.

surplus = income − expenses

surplus > 0 ⇒ money left over
surplus < 0 ⇒ a deficit — you are overspending

Worked ExampleIf transport rises to R1 300 and nothing else changes, what happens?

1
New total = R6500 − 900 + 1 300 = R6900.
Swap the old transport figure for the new one.
2
Surplus = 6500 − 6900 = −R400.
3
That is a deficit of R400 — something else must be cut.
You cannot spend more than you earn month after month.

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Savings belongs in the budget as an expense, not as whatever happens to be left over. Budgeting it first is what makes it actually happen.

Practice exercises

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

📄 Worksheet ✅ Memo 📝 Exam paper 🗝️ Marking guide

1
Calculate the simple interest on R4 000 at 7,5% p.a. for 3 years.
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4 000 × 0,075 × 3 = R900
2
Calculate the total amount in the account after those 3 years.
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4 000 + 900 = R4900
3
Calculate the simple interest on R1 500 at 6% p.a. for 4 years.
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1 500 × 0,06 × 4 = R360
4
Write 7,5% as a decimal.
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7,5 ÷ 100 = 0,075
5
Using the budget below, calculate the total monthly expenses.
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2 200 + 1 500 + 900 + 650 + 300 + 950 = R6500
6
Using the budget below, what percentage of the income goes on rent?
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2 2006500 × 100 = 33,8%
7
Using the budget below, calculate the surplus.
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6500 − 6500 = R0 — the budget balances exactly
8
If transport rises from R900 to R1 300 and nothing else changes, calculate the new surplus.
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6500 − 6900 = −R400, a deficit
9
What does it mean if a budget shows a deficit?
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Expenses are more than income — you are spending money you do not have.