MAT8 Q2W8D4: Applying Financial Problem-Solving Skills

By the end of the lesson, you will be able to:

1. Compute and compare monthly budgets with at least four categories (income, fixed, variable, savings) and determine surplus or deficit correctly in 8 of 10 cases.
2. Decide between saving-then-buy and installment options by calculating total cost and, when applicable, simple interest using $I=P\times r\times t$ and justify the choice with a numeric criterion in 3 short explanations.
3. Create a one-month budget plan that meets a stated savings target, showing adjustments that remove any deficit and documenting computations in MathML.

• Income - money received within a period.
• Fixed expense - cost that does not change with usage.
• Variable expense - cost that changes with usage.
• Savings target - the amount you plan to set aside in a period.
• Surplus - difference when income is more than expenses: $\mathrm{Surplus}=\mathrm{Income}-\mathrm{Expenses}$.
• Deficit - difference when expenses are more than income: $\mathrm{Deficit}=\mathrm{Expenses}-\mathrm{Income}$.
• Budget - a plan that allocates expected income to expense categories and savings.
• Simple interest - interest on principal only: $I=P\times r\times t$, amount $A=P+I$.
• Average balance estimate - approximate mean balance used to estimate interest over part of a year.
• Installment - paying a purchase over time in parts; total may include fees or interest.
• Total cost - all payments including fees: $\text{Total cost}=\text{Base payments}+\text{Fees}$.
• Opportunity cost - the best alternative you give up when you choose something.

1. Classify each: allowance, rent, snacks, data load.
   Show Answer

   Income: allowance. Fixed expense: rent. Variable expense: snacks, data load.

2. Convert 5 months to years.
   Show Answer

   $t=\frac{5}{12}$

3. Write the simple interest formula.
   Show Answer

   $I=P\times r\times t$

What a budget really is

A budget is a plan for a time period, usually a month, that shows how you expect to use your income. A good student budget lists income sources, separates fixed and variable expenses, sets a savings target, and checks if there is a surplus or deficit.

• Income is money you receive in the month.
• Fixed expenses stay the same regardless of usage.
• Variable expenses change with usage.
• Savings target is money set aside for a goal.
• Surplus and deficit compare plan totals to income.

We will use small formulas.

Total expenses $\text{Total expenses}=\text{Fixed}+\text{Variable}$

Surplus or deficit $\mathrm{Surplus}=\mathrm{Income}-\mathrm{Expenses}$, $\mathrm{Deficit}=\mathrm{Expenses}-\mathrm{Income}$

Savings check $\text{Planned savings}\le \text{Possible savings}=\mathrm{Income}-\mathrm{Expenses}$

Checkpoint A1 - Read a tiny budget

You receive ₱3200 this month. Fixed: ₱800 and ₱200. Variable: food ₱1200, transport ₱600, data ₱250. Savings ₱300. Compute the surplus or deficit.

Show Answer

Fixed: $800+200=1000$

Variable: $1200+600+250=2050$

Expenses: $1000+2050=3050$

Plan with savings = 3050 + 300 = 3350. Deficit: $3350-3200=150$

---

Adjusting a budget to hit a savings target

When there is a deficit, reduce variable expenses or adjust categories to remove the gap. State the goal and the gap first.

$\mathrm{Gap}=\text{Total plan}-\mathrm{Income}$

Example B1 - Tighten variable expenses

Income ₱3500. Fixed 900 and 250. Variable: 1300, 700, 250. Savings 400. What is the gap and a one-move fix that keeps savings.

Show Answer

Fixed: $900+250=1150$

Variable: $1300+700+250=2250$

Expenses 3400. Plan 3800. Gap 300. Cut 300 across variables to fit. New plan equals income.

Example B2 - Keep food realistic, trim elsewhere

Show Answer

Variable allowance for plan: $3500-(1150+400)=1950$

Keep food 1300, split remaining to transport and data, for example 550 and 100 to fit 1950.

---

Building your own one-month budget

Checkpoint C1 - Practice

Income: 1800 and 1200. Fixed 300. Variable 1250, 500, 200, 180. Savings 400.

Show Answer

Income: $1800+1200=3000$

Variable 2130. Expenses 2430. Plan 2830. Surplus 170.

Raise savings to 550 - surplus becomes 20.

Show Answer

Plan 2980. Surplus 20.

---

Simple interest - fast and clear

Interest: $I=P\times r\times t$, Amount: $A=P+I$

Months to years: $t=\frac{\text{months}}{12}$

Percent to decimal: $\text{decimal}=\frac{\text{percent}}{100}$

Example D1 - Three-month saving

Show Answer

t = $\frac{3}{12}=0.25$, r = 0.03. I = $5000\times 0.03\times 0.25=37.5$, A = 5037.5

Example D2 - Nine-month saving

Show Answer

I = $8000\times 0.025\times 0.75=150$

---

Save-then-buy versus installment

Example E1 - Headphones decision

Show Answer

Installment total 3720. Saving earns about ₱9; cash 3600. Saving cheaper; installment gives immediate use.

Example E2 - Mid-fee phone plan

Show Answer

Installment 10050. Saving interest about 72. Saving cheaper by 450.

---

Planning a goal with budget and interest

Example F1 - Review class fee

Show Answer

800 × 3 = 2400. Average principal 1200, t 0.25, r 0.02, interest ≈ 6, amount 2406.

---

Real-life budget scenarios

Scenario G1 - Student commuter with pass

Show Answer

Total rides 46. Pay-per-ride 828. Pass 720 is cheaper. With savings 400, plan 3270, surplus 30.

Scenario G2 - Family purchase

Show Answer

Installment total 2520. Saving earns about 9. Saving cheaper by about 129 effective.

---

Decision templates

Use short steps to compare options with numbers and a clear decision.

---

Mixed application problems

Problem I1 - New shoes budget

Show Answer

Deficit 250. Reduce fun 250 to 0 to balance and keep savings 400.

Problem I2 - School device two options

Show Answer

Installment 12360. Saving interest 60. Saving cheaper by 360 plus small interest.

Problem I3 - Semester budget goal

Show Answer

Possible monthly savings 300. Needed per month 600. Not possible without changes.

Problem I4 - Simple interest practice

Show Answer

I = $9000\times 0.025\times 1.25=281.25$

Problem I5 - Budget with pass decision

Show Answer

Pay-per-ride creates 162 deficit. Pass creates 10 deficit; trim 10 to balance.

---

Staggered deposits interest

Example J1 - Unequal deposits

Show Answer

Total interest ≈ 12.5 after 3 months.

---

Explain your choice clearly

Practice K1 - Write it

Show Answer

Goal, numbers, decision. Installment 10050. Saving earns 72 and costs 9600. Choose saving if no urgency.

---

Common mistakes and quick fixes

Checkpoint M1 - Spot and correct

Show Answer

Wrong time unit. Correct t = 0.5. Use average principal 1500, interest 22.5 not 540.

---

Try-write-explain mini tasks

Task N1 - Balance and decide

Show Answer

Deficit 30. Reduce data by 30 or transport by 30 to balance.

Task N2 - Simple interest check

Show Answer

I = $4500\times 0.04\times \frac{1}{6}=30$, A = 4530

Task N3 - Constraint check

Show Answer

Both options violate buffer in month 1 unless you trim 950. Saving is still cheaper in total cost after trimming.

---

Mini reference guide

• Expenses $\text{Expenses}=\text{Fixed}+\text{Variable}$
• Surplus $\mathrm{Surplus}=\mathrm{Income}-\mathrm{Expenses}$
• Installment total $\text{Total}=(\frac{\text{Cash price}}{\text{Months}}+\text{Fee})\times \text{Months}$
• Simple interest $I=P\times r\times t$, $A=P+I$
• Average principal estimate is about half the goal for even monthly saving.

References

• Basic consumer mathematics resources that cover budgets, unit rates, and simple interest.
• Household budgeting guides with examples of fixed versus variable expenses.
• Introductory personal finance materials on saving strategies and simple interest calculations.

Worked Example 1 - Balance a budget with target

Show Answer

Totals: fixed 1150, variable 2150, plan 3700, deficit 100. Cut 100 from one variable to balance.

Worked Example 2 - Pass versus pay-per-ride

Show Answer

Total rides 52. Pass cheaper by 228. With a small 30 cut, plan balances.

Worked Example 3 - Simple interest short period

Show Answer

I = $6000\times 0.03\times \frac{5}{12}=75$, A = 6075

Worked Example 4 - Installment versus saving

Show Answer

Installment 8580. Saving earns about 28 and cash 8400. Saving cheaper by about 180.

Worked Example 5 - Budget with required buffer

Show Answer

Initial plan cannot keep buffer. After trims, max savings becomes 960 while keeping buffer.

1. Balance with target.
   Show Answer

   Surplus 10. Balanced.

2. Exact cut to balance.
   Show Answer

   Deficit 50. Cut exactly 50 from a variable category.

3. Maximum savings with buffer.
   Show Answer

   Max savings 170.

4. Simple interest for months.
   Show Answer

   I = 148.75, A = 8648.75.

5. Installment versus saving.
   Show Answer

   Saving cheaper by about 337.5 effective advantage.

6. Pass threshold inside a budget.
   Show Answer

   Pass fits with 130 surplus.

7. Required monthly saving to hit a goal.
   Show Answer

   Need 900 per month, only 530 possible. Not possible without changes.

8. Price change shock.
   Show Answer

   New food 1378. Cut 78 elsewhere to balance.

9. Unequal deposits interest estimate.
   Show Answer

   Total interest about 9.

10. Short justification with numbers.
    Show Answer

    Pay-per-ride 2052. Pass 2100. Pass is more expensive by 48, choose pay-per-ride.

1. Identify categories.
   Show Answer

   Income: weekend job, scholarship. Fixed: rent. Variable: snacks, data.

2. Compute surplus or deficit.
   Show Answer

   Deficit 30.

3. Exact cut to balance.
   Show Answer

   Reduce one variable by 30 to balance.

4. Maximum savings with buffer.
   Show Answer

   Maximum 400.

5. Simple interest months to years.
   Show Answer

   I = 140, A = 7140.

6. Installment total with fee.
   Show Answer

   Total 8325.

7. Save-then-buy interest estimate.
   Show Answer

   Interest ≈ 20.

8. Decide: save or installment.
   Show Answer

   Saving cheaper by about 432 effective.

9. Rides threshold.
   Show Answer

   Break even at 40 rides; 41 or more buy pass.

10. Budget shock adjustment.
    Show Answer

    New data 253. Cut 23 elsewhere.

11. Multi-source income.
    Show Answer

    Total 2550. Savings 382.5.

12. Simple interest longer time.
    Show Answer

    I = 60.

13. Mini budget and check.
    Show Answer

    Deficit 50. Cut data by 50 to balance.

14. Unequal deposit interest.
    Show Answer

    Total ≈ 8.75.

15. Explain your choice.
    Show Answer

    Installment 8580. Saving earns about 28 and cash 8400. Choose saving if time is acceptable.

1. Two-stage save then buy versus installment with upfront fee.
   Show Answer

   Saving effective outlay ≈ 2793.75. Installment with fee ≈ 3189.99. Saving cheaper by ≈ 396.24.

2. Envelope system with what-if shock.
   Show Answer

   After 5 percent fare hike, transport 630, plan still under income with 90 surplus to allocate.

3. Mid-period rate change on savings.
   Show Answer

   Total interest ≈ 18.75.

4. Break-even monthly fee for installment.
   Show Answer

   Without saving interest: f = 0. With saving interest: effective break-even requires negative fee about −18.75, which means saving remains cheaper.

5. Feasible budget with dual constraints.
   Show Answer

   One feasible plan: expenses 3200 with data 300 and savings 400, leaving 600 buffer, which satisfies all constraints.

Write in your notebook:

• 3 things I can do next month to keep my plan balanced while still saving.
• 2 numbers from today that changed my decision about saving versus installments, and why.
• 1 specific action I will take this week to move toward my savings target.