Number and algebra · Lesson 7 of 7

Money, budgets and simple interest

Wages, pay periods, budgets and interest look like four topics. They are two moves: multiply a rate by an amount, and keep a running total that adds up.

About 20 min · Interactive · 8 practice questions

The interest clock shows a sum of money as a navy bar and the interest it earns as gold blocks, one block per year. Change the money, the rate or the time and watch the blocks change.

Interest per year$200.00
Total interest$600.00
Total amount$5,600.00
Time
4%

Every money question is two moves

Most people meet wages, budgets, interest and bills as separate topics with separate formulas. Instead of four topics, the test is really asking the same two things in different clothes.

Move one: multiply a rate by how much of something you have. An hourly rate times hours gives pay. A rate per year times years gives interest. The rate is a price for one unit, and you are buying several units.

Move two: keep a running total that must add up. Income minus every expense leaves what is left. A deposit plus every instalment makes the price. If the pieces do not add to the whole, something is missing, and the question is usually asking for the missing piece.

Interest is move one in disguise. "6% p.a. for 3 years" means 6 cents on every dollar, three times over. Nobody needs a formula for that: 6 cents times the number of dollars, then times 3.

Practical consequence: write the unit next to every number. "$24.50 per hour × 30 hours" leaves dollars because hours cancel. "4% per year × 18 months" does not cancel until you turn months into years. If the units do not cancel to dollars, the method is wrong.

A fortnightly income of $1,800 shown as a stacked bar split into rent, food, transport, bills and savings with percentages Fortnightly income $1 800 = 100%. The blocks must add to the whole bar. Rent$700 Food$400 Bills$250 Savings$300 Transport $150 700 ÷ 180038.9% 400 ÷ 180022.2% 8.3% 250 ÷ 180013.9% 300 ÷ 180016.7% Check: 700 + 400 + 150 + 250 + 300 = 1 800, and 38.9 + 22.2 + 8.3 + 13.9 + 16.7 = 100%
Every percentage is the line divided by the income, not by the other expenses. The five percentages add to 100% (allowing for rounding), which is the check that nothing is missing.

The eight money methods

Each card is one recipe. Lesson 4 covered discounts, GST and percentage change, so those are not repeated here; this lesson is about earning, spending and borrowing.

1. Wages and overtime

  1. Base pay = hourly rate × ordinary hours.
  2. Overtime rate = hourly rate × 1.5 (time-and-a-half) or × 2 (double time).
  3. Overtime pay = overtime rate × overtime hours only.
  4. Gross pay = base pay + overtime pay.

$24.50/h, 38 h plus 4 h at time-and-a-half: 24.50 × 38 = $931; 24.50 × 1.5 = $36.75/h; 36.75 × 4 = $147; gross $1 078.

2. Salary to a pay period

  1. Weekly = annual ÷ 52.
  2. Fortnightly = annual ÷ 26.
  3. Monthly = annual ÷ 12.
  4. A month is not 4 weeks. 52 weeks ÷ 12 months is 4.33 weeks a month.

$78 000 p.a.: ÷ 52 = $1 500/week; ÷ 26 = $3 000/fortnight; ÷ 12 = $6 500/month (not 4 × 1 500 = $6 000).

3. Budgets

  1. Add every expense line to get total expenses.
  2. Income − total expenses = surplus (positive) or deficit (negative).
  3. Share of income on a line = line ÷ income × 100.

Income $1 800; expenses 700 + 400 + 150 + 250 = $1 500; surplus $300. Rent share: 700 ÷ 1800 × 100 = 38.9%.

4. Simple interest

  1. Turn the time into years first: months ÷ 12, days ÷ 365.
  2. I = P × R × T ÷ 100 (principal × rate × years, then ÷ 100 because the rate is a percentage).
  3. Total amount A = P + I.

$2 400 at 5% for 18 months: T = 1.5; I = 2400 × 5 × 1.5 ÷ 100 = $180; A = $2 580.

5. Finding the rate or the time

  1. Same formula, rearranged: R = 100 × I ÷ (P × T).
  2. T = 100 × I ÷ (P × R), answer in years.
  3. Check by putting the answer back into I = PRT ÷ 100.

$90 interest on $1 500 over 2 years: R = 9000 ÷ (1500 × 2) = 9000 ÷ 3000 = 3% p.a.

6. Loan repayments

  1. Work out the simple interest for the whole loan.
  2. Total to repay = principal + interest.
  3. Repayment per month = total ÷ number of months.

$6 000 at 8% p.a. over 2 years: I = $960; total $6 960; 24 months → $290 per month.

7. Bills, splits and instalments

  1. Equal split: total ÷ number of people.
  2. Deposit + (number of instalments × instalment) = total price.
  3. To find the instalment: (total − deposit) ÷ number of instalments.

$1 160 laptop, $200 deposit, 12 instalments: (1160 − 200) ÷ 12 = $80 each.

8. Compound interest (not tested)

  1. Compound interest is interest on interest: each year's interest is added to the principal before the next year is worked out.
  2. The test uses simple interest unless a question says otherwise.

If a question says "simple interest" or just "interest at 4% p.a.", use I = PRT ÷ 100.

Money solver that shows its working

Pick a problem type and enter the numbers

Every step is shown with its unit, so you can see where hours or months cancel. Money is rounded to the cent at the end, not in the middle.

Time
Time
Loan length

    Why simple interest is a straight line

    Simple interest is worked out on the original principal every year, so each year adds the same amount. The same amount added each year draws a straight line. That is the whole reason the formula has a plain multiplication by T in it.

    Compound interest adds each year's interest to the principal before working out the next year, so the yearly step grows. That draws a curve. The test does not ask you to calculate it; it is drawn here only so the word "simple" makes sense.

    Growth of $5,000 at 4% per year over 5 years: simple interest is a straight line rising $200 each year; a faint compound curve rises slightly faster $5 000$5 200$5 400$5 600$5 800$6 000 012345 years compound: interest on interest (not tested; shown so "simple" makes sense) +$200+$200+$200+$200+$200 simple: $6 000 after 5 years
    $5 000 at 4% p.a. earns 4% of $5 000 = $200 every year, so the simple-interest line climbs by the same $200 step each year and reaches $6 000. The faint dashed curve is compound growth, which reaches about $6 083; it is not tested.

    Numbers to know by heart

    These conversions come up in nearly every money question. Knowing them saves a step, and in the non-calculator section it saves the question.

    ItemValueHow to remember it
    Time in years (for interest)
    6 months0.5 yearsHalf a year
    3 months0.25 yearsA quarter: 3 ÷ 12
    9 months0.75 yearsThree quarters
    18 months1.5 yearsA year and a half
    73 days0.2 years365 ÷ 5 = 73, so one fifth
    146 days0.4 yearsTwo lots of 73
    Pay-period divisors (annual ÷ …)
    Weekly÷ 5252 weeks in a year
    Fortnightly÷ 26Half of 52
    Monthly÷ 1212 months, never "4 weeks"
    Hourly (38-hour week)÷ 1 97638 × 52 = 1 976 hours a year
    Overtime multipliers
    Time-and-a-half× 1.5The rate plus half of it again
    Double time× 2Twice the rate
    Double-and-a-half× 2.5Twice the rate plus half
    Quick percentages of money
    10% of $xMove the decimal point one place left10% of $640 = $64
    5% of $xHalf of 10%5% of $640 = $32
    2.5% of $xHalf of 5%2.5% of $640 = $16

    Hide a column, say each answer aloud, then click a striped cell to check it.

    Payslip drill

    Eight quick rounds. Odd rounds show a casual payslip and ask for the gross pay; even rounds give a deposit and ask for the simple interest. Type the dollar amount; cents are fine.

    Round 1 of 8

    Score 0 · streak 0

    Common traps

    • Months straight into the formula. "18 months at 5%" with T = 18 gives twelve times too much interest. The rate is per year, so T must be in years: 18 ÷ 12 = 1.5.
    • Interest instead of the total. I is what is earned; A = P + I is what is in the account. Read whether the question wants "the interest" or "the amount".
    • Dividing a salary by 48, or calling a month 4 weeks. A year has 12 months and 52 weeks, so a month is 4.33 weeks. $1 500 a week is $6 500 a month, not $6 000.
    • Overtime multiplier on every hour. Time-and-a-half applies only to the overtime hours. Work out the ordinary hours at the ordinary rate and add the overtime separately.
    • Percentage of the wrong whole. "What percentage of income goes on rent?" divides by income, not by total expenses. Check what the question says "of".
    • Forgetting the deposit. A $200 deposit plus 12 instalments of $65 costs $980, not $780. The instalments are only part of the price.
    • Rounding each line before adding. Round a budget or payslip once, at the end. Rounding every line first can shift the total by several cents and miss the answer key.

    ACER-style practice

    Eight questions in the formats the real test uses: multiple choice, type your answer, and true-or-false tables. Questions marked "no calculator" belong to the test's final section, where you cannot use one. Check each answer for a full explanation.

    0 of 8 checked

    What to remember

    • Money questions are a rate × an amount, plus a running total that must add up.
    • Wages: rate × ordinary hours + rate × multiplier × overtime hours. The multiplier touches only the overtime hours.
    • Salary: ÷ 52 weekly, ÷ 26 fortnightly, ÷ 12 monthly. A month is 4.33 weeks, not 4.
    • Budget: income − expenses = surplus; a line's share is line ÷ income × 100.
    • Simple interest: I = P × R × T ÷ 100 with T in years; months ÷ 12, days ÷ 365. Amount A = P + I.
    • Rearranged: R = 100I ÷ (PT), T = 100I ÷ (PR). Put the answer back in to check.
    • Instalments: deposit + n × instalment = total. Loan repayment per month = (P + I) ÷ months.

    All questions on this page are original and are not reproduced from ACER material. LANTITE is administered by the Australian Council for Educational Research.