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hscscience Maths Std · Y11
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Module 3 · L14 of 14 ~50 min MST-11-04 ⚡ +90 XP available

Saving, Emergency Funds and Monitoring Spending

A budget tells you what should happen. An emergency fund decides whether one bad month becomes a crisis. Monitoring tells you which of the two you are actually living. Build all three as a spreadsheet, then work out how long the fund takes to fill and what a small overspend really costs you.

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Learning Intentions

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Think First

Someone earns $\$4{,}200$ a month and spends $\$2{,}960$, so they save $\$1{,}240$ every month. Their car needs $\$2{,}000$ of repairs with no warning. Are they fine? Write down your answer, then write down the one number you would need to know before you could actually be sure.

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Learning Intentions

Model a personal budget in a spreadsheet, separating fixed from discretionary spending
Calculate the monthly surplus and express it as a savings rate
Work out living expenses and size an emergency fund at 3 to 6 months of them
Calculate how many months of saving a fund takes to build, rounding up
Compare actual spending against the budget and explain what a variance costs
Justify which strategy suits a given person, using your own figures
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Key Terms

Fixed spendingCosts that are the same each month whatever you do, so they are the hardest to cut quickly. Like this: rent $\$1{,}450$, insurance $\$120$, phone $\$55$, a transport pass $\$195$ and subscriptions $\$40$ come to $\$1{,}860$ every month.
Discretionary spendingCosts you choose, which can be reduced at short notice. Like this: groceries $\$620$, eating out $\$250$, entertainment $\$140$ and clothing $\$90$ come to $\$1{,}100$, and three of those four could be cut next month.
SurplusIncome minus total spending: what is left over to save. Like this: $4200 - 2960 = \$1{,}240$ a month, and if that number is negative it is a deficit rather than a surplus.
Savings rateThe surplus as a percentage of income, so two people on different salaries can be compared. Like this: $\dfrac{1240}{4200} \times 100 = 29.5\%$ (to one decimal place).
Living expensesWhat it costs to keep going if income stops: fixed spending plus the essentials only, not everything you normally spend. Like this: $\$1{,}860$ fixed plus $\$620$ groceries is $\$2{,}480$, and eating out is not in it.
Emergency fundSavings held aside to cover 3 to 6 months of living expenses if income stops or a large unplanned cost arrives. Like this: at $\$2{,}480$ a month that is $\$7{,}440$ for three months and $\$14{,}880$ for six.
VarianceActual spending minus budgeted spending, positive when you overspent. Like this: budgeting $\$620$ for groceries and spending $\$682$ is a variance of $+\$62$, which is 10% over.
Monitoring spendingComparing actual against budget every month so a drift is caught while it is still small. Like this: an overspend of only $\$60$ a month adds a whole extra month to filling a $\$7{,}440$ fund.
A budget shows income $\$4{,}200$, fixed spending $\$1{,}860$ and discretionary spending $\$1{,}100$ per month. What is the monthly surplus?
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The Budget As A Spreadsheet

A budget is income, minus what you must pay, minus what you choose to pay.

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The Budget As A Spreadsheet

A budget is income, minus what you must pay, minus what you choose to pay. Splitting the spending into fixed and discretionary is the whole point: it separates what you cannot change next month from what you can.

Built as a model, with every input in its own cell:

AB
1Net income per month4200
3Rent1450
4Insurance120
5Phone55
6Transport pass195
7Subscriptions40
8Total fixed=SUM(B3:B7)
10Groceries620
11Eating out250
12Entertainment140
13Clothing90
14Total discretionary=SUM(B10:B13)
16Total spending=B8+B14
17Surplus=B1-B16
18Savings rate=B17/B1

B8 returns $\$1{,}860$ and B14 returns $\$1{,}100$, so B16 is $\$2{,}960$ and B17 is $4200 - 2960 = \$1{,}240$. B18 gives $\dfrac{1240}{4200} = 0.2952$, a savings rate of $29.5\%$ to one decimal place.

The reason to build it rather than calculate it once is the question you can now ask: change B11 from $250$ to $150$ and every figure below updates, so you can see immediately what cutting one habit is worth.

Must do: Use NET income, what actually lands in the account, not the salary before tax. A budget built on gross income overstates the surplus by the whole tax bill.
Common error: Putting the surplus in as a typed number. The moment any cost changes, a typed surplus stops matching its own inputs and nothing on screen shows it has gone stale.

Budget: surplus = income − (fixed + discretionary). Savings rate = surplus / income. Model it with =SUM(B3:B7), =SUM(B10:B13), =B8+B14, =B1-B16, =B17/B1. Income 4,200 less 1,860 fixed and 1,100 discretionary leaves 1,240 a month, a 29.5% savings rate (dollars).

Pause, copy the budget layout into your book with the five formulas exactly as written, and the worked figures beside them: 1,860 fixed, 1,100 discretionary, 2,960 spent, 1,240 surplus.

Living expenses are $\$2{,}480$ a month. A three-month emergency fund is $\$$, and a six-month fund is $\$$.
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Sizing An Emergency Fund

An emergency fund is money set aside to cover 3 to 6 months of living expenses if income stops or a large unplanned cost arrives.

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Sizing An Emergency Fund

An emergency fund is money set aside to cover 3 to 6 months of living expenses if income stops or a large unplanned cost arrives. Two calculations, and one judgement.

First, living expenses are not total spending. If income stopped tomorrow you would still pay rent and eat, but you would stop eating out and cancel entertainment. From the budget in Card 1:

  • Fixed spending $\$1{,}860$, all of it unavoidable in the short term.
  • Plus groceries $\$620$, which is discretionary but essential.
  • Living expenses $= 1860 + 620 = \$2{,}480$ per month.

Eating out, entertainment and clothing come to $250 + 140 + 90 = \$480$, and none of it belongs in the fund. Including it would size the fund on a lifestyle you would not be living.

Second, the target. Three months is $3 \times 2480 = \$7{,}440$; six months is $6 \times 2480 = \$14{,}880$.

Third, how long it takes. Saving the whole $\$1{,}240$ surplus each month:

  • Three-month fund: $7440 \div 1240 = 6$ months.
  • Six-month fund: $14880 \div 1240 = 12$ months.

When the division is not exact, round up. You cannot part-fund a month: $6.3$ months means the target is not reached until month 7.

Must do: Build the fund on living expenses, not on income and not on total spending. Sizing it on the $\$2{,}960$ you spend rather than the $\$2{,}480$ you would need gives a target $\$1{,}440$ too high for three months.
Common error: Rounding the months down. $5.8$ months of saving has not reached the target, so the answer is 6.

Living expenses = fixed + essential discretionary only. Emergency fund = 3 to 6 x living expenses. Months to build = target / monthly surplus, ROUNDED UP. At 2,480 a month: 7,440 for three months, 14,880 for six, and 6 or 12 months to build at a 1,240 surplus (dollars).

Pause, copy the three steps into your book (living expenses, target, months to build) with the worked numbers: 2,480 a month, 7,440 and 14,880, 6 and 12 months.

True or False: an emergency fund should cover 3 to 6 months of everything you normally spend, including eating out and entertainment.
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Monitoring: Budget Against Actual

A budget is a plan.

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Monitoring: Budget Against Actual

A budget is a plan. Monitoring is checking whether you lived it. Each month you record what you actually spent next to what you budgeted, and the difference is the variance:

variance = actual $-$ budget, positive when you overspent.

Take one month against the Card 1 budget:

CategoryBudgetActualVariance
Groceries620682+62
Eating out250205−45
Entertainment140183+43
Clothing90900
Net11001160+60

Groceries ran 10% over ($\dfrac{62}{620} \times 100 = 10\%$) and eating out came in 18% under ($\dfrac{45}{250} \times 100 = 18\%$). They partly cancel, and the net is $+62 - 45 + 43 + 0 = +\$60$.

Sixty dollars sounds like nothing. Follow it through: spending rises to $\$3{,}020$, so the surplus falls to $4200 - 3020 = \$1{,}180$, and the three-month fund now takes $7440 \div 1180 = 6.3$, which rounds up to 7 months instead of 6.

That is what monitoring buys you. The overspend is invisible in a bank balance and obvious in a variance column, and one month of noticing it is the difference between a six-month plan and a seven-month one.

Must do: Keep the sign. A $-\$45$ variance is money saved and a $+\$62$ variance is money spent; adding them without signs gives $\$107$ of drift where the real figure is $\$17$ for those two lines.
Common error: Judging a month by the biggest single variance. Entertainment was 31% over and only $\$43$; groceries were 10% over and $\$62$. The percentage says how far off the estimate was, the dollars say what it cost.

Variance = actual − budget, positive means overspent. Keep the signs and add them: +62 − 45 + 43 + 0 = +60. A 60 overspend cuts the surplus from 1,240 to 1,180 and pushes a 7,440 fund from 6 months to 7 (dollars).

Pause, copy the variance formula and the four-row table into your book, and write underneath what the +60 did to the number of months.

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Which Strategy, And Why

The syllabus asks you to examine budgeting, saving, an emergency fund and monitoring as strategies designed to minimise...

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Which Strategy, And Why

The syllabus asks you to examine budgeting, saving, an emergency fund and monitoring as strategies designed to minimise financial problems. They are not interchangeable: each one answers a different question.

  • A budget answers "can this income cover this life?". It prevents the slow problem of spending slightly more than you earn.
  • An emergency fund answers "what if income stops?". It prevents the sudden problem, where a $\$2{,}000$ repair becomes debt because nothing was set aside.
  • Monitoring answers "am I living the plan?". It is what tells you a budget has quietly stopped being true.

Choosing the fund size is a judgement about risk, and the numbers only support it:

  • Stable, salaried, one earner in a secure job: three months, $\$7{,}440$, reached in 6 months at a $\$1{,}240$ surplus.
  • Casual or variable hours, or a single income supporting others: six months, $\$14{,}880$, reached in 12 months.

The difference is $\$7{,}440$, which at $\$1{,}240$ a month is six extra months of saving. That is a real cost, and it buys a real thing: twice as long to find work before the fund runs out. A full-mark justification says both, in numbers.

Must do: Quote your own figures. "A casual worker should save more" earns little; "six months is $\$14{,}880$ against $\$7{,}440$, six extra months of saving, because casual hours can fall without notice" earns the mark.
Common error: Treating the emergency fund as the whole answer. A fund with no monitoring drains quietly, and a budget nobody checks stops matching reality within a few months.

Budget answers can this income cover this life. Emergency fund answers what if income stops. Monitoring answers am I living the plan. Fund size is a risk judgement: 3 months for stable income, 6 for casual or variable, and the gap is 7,440 or six extra months of saving.

Pause, copy the three strategies into your book with the question each one answers, and write one sentence on which fund size you would choose for a casual worker and why.

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Worked examples · reveal each step

Worked examples · reveal each step

Worked examples · reveal each step

WE1 · Building the budget. Net income is $\$3{,}600$ a month. Fixed: rent $\$1{,}300$, insurance $\$95$, phone $\$45$, transport $\$160$. Discretionary: groceries $\$540$, eating out $\$180$, entertainment $\$110$, other $\$70$. Find the surplus and the savings rate.
Total fixed $= 1300 + 95 + 45 + 160 = \$1{,}600$.
Total discretionary $= 540 + 180 + 110 + 70 = \$900$.
Total spending $= 1600 + 900 = \$2{,}500$.
Surplus $= 3600 - 2500 = \mathbf{\$1{,}100}$ per month.
Savings rate $= \dfrac{1100}{3600} \times 100 = \mathbf{30.6\%}$ (1 d.p.).
WE2 · Sizing and filling the fund. Using WE1, groceries are the only essential discretionary item. Find the three-month and six-month fund targets, and how long each takes to build.
Living expenses $= 1600 + 540 = \$2{,}140$ per month.
Three-month target $= 3 \times 2140 = \mathbf{\$6{,}420}$. Six-month target $= 6 \times 2140 = \mathbf{\$12{,}840}$.
At a surplus of $\$1{,}100$: $6420 \div 1100 = 5.84$, which rounds up to $\mathbf{6}$ months.
And $12840 \div 1100 = 11.67$, which rounds up to $\mathbf{12}$ months.
Both round up, because at month 5 the fund holds $5 \times 1100 = \$5{,}500$, which is short of $\$6{,}420$ ✓.
WE3 · A month of monitoring. Against WE1's budget the actuals were: groceries $\$594$, eating out $\$153$, entertainment $\$143$, other $\$70$. Find each variance, the net variance, and the effect on the time to build the three-month fund.
Groceries: $594 - 540 = +\$54$, which is $\dfrac{54}{540} \times 100 = 10\%$ over.
Eating out: $153 - 180 = -\$27$, which is $15\%$ under. Entertainment: $143 - 110 = +\$33$, which is $30\%$ over. Other: $70 - 70 = \$0$.
Net variance $= 54 - 27 + 33 + 0 = +\$60$.
Spending becomes $2500 + 60 = \$2{,}560$, so the surplus falls to $3600 - 2560 = \mathbf{\$1{,}040}$.
Time to the $\$6{,}420$ target $= 6420 \div 1040 = 6.17$, which rounds up to $\mathbf{7}$ months, one month later than WE2.
Entertainment was the worst percentage at 30% and only $\$33$; groceries were 10% over and cost $\$54$. Percentages rank the estimate, dollars rank the damage.
WE4 · Justifying the fund size. Two people have identical living expenses of $\$2{,}480$ a month and identical surpluses of $\$1{,}240$. Ana is salaried in a secure role. Ben works casual hours that vary week to week. Recommend a fund size for each and justify it.
Ana, three months: $3 \times 2480 = \$7{,}440$, reached in $7440 \div 1240 = 6$ months.
Ben, six months: $6 \times 2480 = \$14{,}880$, reached in $14880 \div 1240 = 12$ months.
The extra cost to Ben is $14880 - 7440 = \$7{,}440$, which is $7440 \div 1240 = \mathbf{6}$ extra months of saving.
Justification: Ana's income is predictable, so three months is enough to cover a gap between jobs or a single large cost. Ben's hours can fall without notice and may recover slowly, so he needs the longer runway even though it costs him six more months of saving to get there.
Note what is doing the work. The arithmetic is identical for both; the recommendation differs entirely on the stability of the income, which is why the syllabus asks you to justify rather than just calculate.
A three-month fund target is $\$7{,}440$ and the monthly surplus is $\$1{,}180$. How many months of saving are needed?
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