Practice Questions

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Time Value of Money Problems

Question 1: Present Value

You will receive 10,000 baht one year from now. If the discount rate is 5% per year, what is the current value?

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Formula:

PV = FV / (1 + r)ᵗ

Given:

• FV = 10,000 baht
• r = 5% = 0.05
• t = 1 year

Calculation:

PV = 10,000 / (1 + 0.05)¹
PV = 10,000 / 1.05
PV = 9,523.81 baht

✅ Answer: 9,523.81 baht

Question 2: Present Value (Multi-Year)

A payment of 50,000 baht is due in 3 years. The discount rate is 4%. What is the PV?

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Formula:

PV = FV / (1 + r)ᵗ

Given:

• FV = 50,000 baht
• r = 4% = 0.04
• t = 3 years

Calculation:

PV = 50,000 / (1 + 0.04)³
PV = 50,000 / 1.124864
PV = 44,449.82 baht

✅ Answer: 44,449.82 baht

Question 3: Future Value

How much will 10,000 baht grow to in 3 years if the interest rate is 6%?

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Formula:

FV = PV(1 + r)ᵗ

Given:

• PV = 10,000 baht
• r = 6% = 0.06
• t = 3 years

Calculation:

FV = 10,000(1 + 0.06)³
FV = 10,000(1.191016)
FV = 11,910.16 baht

✅ Answer: 11,910.16 baht

Question 4: Future Value (Long-Term)

You invest 50,000 baht at 8% compounded annually. How much will you have after 5 years?

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Formula:

FV = PV(1 + r)ᵗ

Given:

• PV = 50,000 baht
• r = 8% = 0.08
• t = 5 years

Calculation:

FV = 50,000(1 + 0.08)⁵
FV = 50,000(1.469328)
FV = 73,466.40 baht

✅ Answer: 73,466.40 baht

Question 5: Present Value for Goal

An investor wants 200,000 baht in 4 years. If the interest rate is 6%, how much must they deposit today?

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Formula:

PV = FV / (1 + r)ᵗ

Given:

• FV = 200,000 baht (goal)
• r = 6% = 0.06
• t = 4 years

Calculation:

PV = 200,000 / (1 + 0.06)⁴
PV = 200,000 / 1.262477
PV = 158,418.73 baht

✅ Answer: 158,418.73 baht

Interpretation: Need to deposit 158,418.73 baht today to have 200,000 baht in 4 years at 6% interest.

Question 6: Present Value of Annuity

You will receive 5,000 baht per year for 4 years, discount rate 5%. What is the current value?

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Formula:

PVA = PMT × [1 - 1/(1 + r)ᵗ] / r

Given:

• PMT = 5,000 baht per year
• r = 5% = 0.05
• t = 4 years

Step-by-Step Calculation:

Step 1: Calculate (1 + r)ᵗ

(1 + 0.05)⁴ = 1.215506

Step 2: Calculate 1/(1 + r)ᵗ

1/1.215506 = 0.822702

Step 3: Calculate [1 - 1/(1 + r)ᵗ]

1 - 0.822702 = 0.177298

Step 4: Divide by r

0.177298 / 0.05 = 3.54595

Step 5: Multiply by PMT

PVA = 5,000 × 3.54595
PVA = 17,729.75 baht

✅ Answer: 17,729.75 baht (Ordinary annuity)

Interpretation: The current value of receiving 5,000 baht per year for 4 years is 17,729.75 baht.

Question 7: Future Value of Annuity

You save 15,000 baht per year in a retirement fund earning 5%. How much will you have after 10 years?

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Formula:

FVA = PMT × [(1 + r)ᵗ - 1] / r

Given:

• PMT = 15,000 baht per year
• r = 5% = 0.05
• t = 10 years

Step-by-Step Calculation:

Step 1: Calculate (1 + r)ᵗ

(1 + 0.05)¹⁰ = 1.628895

Step 2: Subtract 1

1.628895 - 1 = 0.628895

Step 3: Divide by r

0.628895 / 0.05 = 12.577893

Step 4: Multiply by PMT

FVA = 15,000 × 12.577893
FVA = 188,668.39 baht

✅ Answer: 188,668.39 baht (Ordinary annuity)

Interpretation: Saving 15,000 baht per year for 10 years at 5% will grow to 188,668.39 baht.

Question 8: Solving for Payment

You want to accumulate 1,000,000 baht in 12 years. You can earn 6% per year, and you will deposit the same amount each year. How much must you deposit each year?

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Formula:

FVA = PMT × [(1 + r)ᵗ - 1] / r

Rearrange to solve for PMT:

PMT = FVA × r / [(1 + r)ᵗ - 1]

Given:

• FVA = 1,000,000 baht (goal)
• r = 6% = 0.06
• t = 12 years

Step-by-Step Calculation:

Step 1: Calculate (1 + r)ᵗ

(1 + 0.06)¹² = 2.012196

Step 2: Subtract 1

2.012196 - 1 = 1.012196

Step 3: Multiply FVA by r

1,000,000 × 0.06 = 60,000

Step 4: Divide

PMT = 60,000 / 1.012196
PMT = 59,277.03 baht

✅ Answer: 59,277.03 baht per year (Ordinary annuity)

Interpretation: You must deposit 59,277.03 baht each year for 12 years at 6% to accumulate 1,000,000 baht.

Financial Ratio Problems

Question 9: Basic Liquidity Ratio

You have $9,000 in liquid assets and monthly expenses of $2,500. Calculate your basic liquidity ratio. Is it adequate?

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Formula:

Basic Liquidity Ratio = Liquid Assets / Monthly Expenses

Given:

• Liquid Assets = $9,000
• Monthly Expenses = $2,500

Calculation:

Ratio = $9,000 / $2,500 = 3.6

✅ Answer: 3.6

Benchmark: ≥ 3.0 (recommended)

Interpretation:

• ✅ **Yes, adequate!** Your ratio of 3.6 exceeds the recommended 3.0
• You can survive **3.6 months** without income using only liquid assets
• This provides a good emergency fund cushion

Question 10: Asset-to-Debt Ratio

Total assets: $75,000. Total liabilities: $45,000. Calculate asset-to-debt ratio. Are you solvent?

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Formula:

Asset-to-Debt Ratio = Total Assets / Total Liabilities

Given:

• Total Assets = $75,000
• Total Liabilities = $45,000

Calculation:

Ratio = $75,000 / $45,000 = 1.67

✅ Answer: 1.67

Benchmark: > 1.0 (must be greater than 1 to be solvent)

Interpretation:

• ✅ **Yes, you are solvent!** Ratio > 1.0 means you own more than you owe
• You own $1.67 for every $1.00 you owe
• Net Worth = $75,000 - $45,000 = $30,000 (positive)

Question 11: Debt Service-to-Income Ratio

Annual debt payments: $22,000. Gross annual income: $70,000. Calculate debt service-to-income ratio. Is it acceptable?

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Formula:

Debt Service-to-Income Ratio = Annual Debt Payments / Gross Annual Income

Given:

• Annual Debt Payments = $22,000
• Gross Annual Income = $70,000

Calculation:

Ratio = $22,000 / $70,000 = 0.314 = 31.4%

✅ Answer: 0.314 (31.4%)

Benchmark: ≤ 0.333 (33.3%) recommended

Interpretation:

• ✅ **Yes, acceptable!** Your ratio of 31.4% is below the recommended 33.3%
• You spend 31.4% of gross income on debt payments
• You have manageable debt levels
• Room for additional debt if needed (but not recommended)

Question 12: Investment Assets Ratio

You are 35 years old. Investment assets: $25,000. Total assets: $100,000. Calculate the ratio. Is it appropriate for your age?

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Formula:

Investment Assets-to-Total Assets Ratio = Investment Assets / Total Assets

Given:

• Age = 35 years old
• Investment Assets = $25,000
• Total Assets = $100,000

Calculation:

Ratio = $25,000 / $100,000 = 0.25 = 25%

✅ Answer: 0.25 (25%)

Benchmark (Age-Based):

• 20s: 10%
• **30s: 11-30%** ← Your age group
• 40s: 30%+
• 50s+: 50%+

Interpretation:

• ✅ **Yes, appropriate for your age!** Your 25% is within the 11-30% range for people in their 30s
• You're on track for retirement savings
• Consider gradually increasing as you approach your 40s

Tax Calculation Problems

Question 13: Marginal Tax Calculation

Taxable income: $45,000 Tax brackets: 10% ($0-$8,350), 15% ($8,351-$33,950), 25% ($33,951+) Calculate total tax liability.

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Given:

• Taxable Income = $45,000
• Tax Brackets:
• 10% on $0 - $8,350
• 15% on $8,351 - $33,950
• 25% on $33,951+

Progressive Tax Calculation (Step-by-Step):

Bracket 1: First $8,350 at 10%

$8,350 × 0.10 = $835.00

Bracket 2: Next $25,600 at 15% ($33,950 - $8,350)

$25,600 × 0.15 = $3,840.00

Bracket 3: Remaining $11,050 at 25% ($45,000 - $33,950)

$11,050 × 0.25 = $2,762.50

Total Tax:

$835.00 + $3,840.00 + $2,762.50 = $7,437.50

✅ Answer: $7,437.50

Additional Info:

• **Marginal Tax Rate:** 25% (last dollar taxed at 25%)
• **Average Tax Rate:** $7,437.50 / $45,000 = 16.5%
• **NOT:** $45,000 × 0.25 = $11,250 ❌ (This is wrong!)

Question 14: Average Tax Rate

Gross income: $55,000. Total taxes paid: $8,250. Calculate average tax rate.

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Formula:

Average Tax Rate = Total Taxes Paid / Gross Income

Given:

• Gross Income = $55,000
• Total Taxes Paid = $8,250

Calculation:

Average Tax Rate = $8,250 / $55,000 = 0.15 = 15%

✅ Answer: 15%

Interpretation:

• You pay 15% of your total income in taxes
• This is your overall tax burden
• Average tax rate is always less than marginal tax rate

Question 15: Tax Credit vs. Deduction

You’re in the 28% marginal tax bracket. Compare:

• Option A: $2,000 tax deduction
• Option B: $2,000 tax credit

Which saves more money?

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Given:

• Marginal Tax Rate = 28%
• Both options = $2,000

Option A: Tax Deduction

Tax Savings = Deduction × Marginal Tax Rate
Tax Savings = $2,000 × 0.28 = $560

Option B: Tax Credit

Tax Savings = Credit Amount (dollar-for-dollar)
Tax Savings = $2,000

Comparison:

Option	Amount	Savings
A: Deduction	$2,000	$560
B: Credit	$2,000	$2,000
Difference		$1,440

✅ Answer: Option B (Tax Credit) is better!

Key Insight:

• Credit saves $2,000
• Deduction saves only $560
• Credit provides **$1,440 more savings**
• Tax credits are always better than deductions of the same amount!

Question 16: 401(k) Tax Savings

You contribute $5,000 to your 401(k). Your marginal tax rate is 25%. How much do you save in taxes?

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Formula:

Tax Savings = Contribution × Marginal Tax Rate

Given:

• 401(k) Contribution = $5,000
• Marginal Tax Rate = 25% = 0.25

Calculation:

Tax Savings = $5,000 × 0.25 = $1,250

✅ Answer: $1,250 in immediate tax savings

Additional Benefits:

• ✅ Your $5,000 grows tax-deferred (no taxes on growth until withdrawal)
• ✅ Employer may match contributions (free money!)
• ✅ Reduces taxable income from gross income
• ✅ Builds retirement savings

Example:

• Without 401(k): Pay taxes on $5,000 = $1,250 in taxes
• With 401(k): Save $5,000 + avoid $1,250 in taxes = Win-win!

Real vs. Nominal Income Problems

Question 17: Real Income Change

Current salary: $45,000. New salary: $47,500. Inflation: 3.5%. Calculate real income change.

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Given:

• Current Salary = $45,000
• New Salary = $47,500
• Inflation Rate = 3.5%

Step 1: Calculate Nominal Change

Nominal Change % = [(New - Old) / Old] × 100
Nominal Change % = [($47,500 - $45,000) / $45,000] × 100
Nominal Change % = ($2,500 / $45,000) × 100
Nominal Change % = 5.56%

Step 2: Calculate Real Change

Real Change % = Nominal Change % - Inflation %
Real Change % = 5.56% - 3.5%
Real Change % = 2.06%

Step 3: Calculate Real Income in Dollars

Real Income = Old Salary × (1 + Real Change as decimal)
Real Income = $45,000 × (1 + 0.0206)
Real Income = $45,000 × 1.0206
Real Income = $45,927

✅ Answer Summary:

Measure	Amount
Nominal raise	$2,500
Real economic progress	$927
Lost to inflation	$1,573
Real change percentage	2.06%

Interpretation:

• You got a $2,500 raise (5.56%)
• But inflation ate $1,573 of it
• Your real purchasing power only increased by $927 (2.06%)

Budgeting Problems

Question 18: Net Worth Calculation

Assets: Checking $2,000, Savings $5,000, Car $15,000, House $200,000 Liabilities: Credit card $3,000, Car loan $8,000, Mortgage $150,000 Calculate net worth.

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Formula:

Net Worth = Total Assets - Total Liabilities

Given Assets:

• Checking account: $2,000
• Savings account: $5,000
• Car: $15,000
• House: $200,000

Given Liabilities:

• Credit card: $3,000
• Car loan: $8,000
• Mortgage: $150,000

Step 1: Calculate Total Assets

Total Assets = $2,000 + $5,000 + $15,000 + $200,000
Total Assets = $222,000

Breakdown:

• Monetary assets: $7,000 (checking + savings)
• Tangible assets: $15,000 (car)
• Investment assets: $200,000 (house)

Step 2: Calculate Total Liabilities

Total Liabilities = $3,000 + $8,000 + $150,000
Total Liabilities = $161,000

Breakdown:

• Short-term: $3,000 (credit card)
• Long-term: $158,000 (car loan + mortgage)

Step 3: Calculate Net Worth

Net Worth = Assets - Liabilities
Net Worth = $222,000 - $161,000
Net Worth = $61,000

✅ Answer: $61,000

Interpretation:

• Your true financial wealth is $61,000
• You are **solvent** (positive net worth)
• Asset-to-debt ratio: $222,000 / $161,000 = 1.38 (good!)

Question 19: Cash Flow Surplus/Deficit

Monthly income: $5,000 Fixed expenses: $2,500 (rent, car payment, insurance) Variable expenses: $1,800 (food, utilities, entertainment) Calculate surplus or deficit.

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Formula:

Surplus (Deficit) = Total Income - Total Expenses

Given:

• Monthly Income = $5,000
• Fixed Expenses = $2,500 (rent, car payment, insurance)
• Variable Expenses = $1,800 (food, utilities, entertainment)

Step 1: Calculate Total Expenses

Total Expenses = Fixed + Variable
Total Expenses = $2,500 + $1,800
Total Expenses = $4,300

Step 2: Calculate Surplus/Deficit

Surplus = Income - Expenses
Surplus = $5,000 - $4,300
Surplus = $700

✅ Answer: $700 surplus (positive cash flow)

What to Do with Surplus:

1. ✅ Build emergency fund (if < 3 months expenses)

2. ✅ Pay down high-interest debt

3. ✅ Invest in retirement account (401k, IRA)

4. ✅ Save for specific goals

5. ✅ Invest in taxable accounts

Budget Breakdown:

• Income: 100%
• Fixed expenses: 50% (reasonable)
• Variable expenses: 36% (good)
• Surplus: 14% (excellent savings rate!)

Rule of 72 Problems

Question 20: Doubling Time

You invest at 9% annual return. How long until your money doubles?

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Formula (Rule of 72):

Years to Double = 72 / Interest Rate

Given:

• Interest Rate = 9%

Calculation:

Years = 72 / 9 = 8 years

✅ Answer: 8 years

Interpretation:

• At 9% annual return, your investment will double in 8 years
• $1,000 → $2,000 in 8 years
• $10,000 → $20,000 in 8 years
• This is a quick mental calculation (actual: 8.04 years)

Verification (using FV formula):

FV = PV(1 + r)ᵗ
$2,000 = $1,000(1.09)⁸
$2,000 = $1,000(1.9926)
$2,000 ≈ $1,993 ✓ (close!)

Question 21: Required Return

You want to double your money in 6 years. What return do you need?

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Formula (Rule of 72 - Rearranged):

Interest Rate = 72 / Years to Double

Given:

• Desired time to double = 6 years

Calculation:

Rate = 72 / 6 = 12%

✅ Answer: 12% annual return needed

Interpretation:

• You need a 12% annual return to double your money in 6 years
• This is relatively high - stock market averages ~10% long-term
• Higher returns usually mean higher risk

Examples at 12%:

• $5,000 → $10,000 in 6 years
• $25,000 → $50,000 in 6 years
• $100,000 → $200,000 in 6 years

Verification (using FV formula):

FV = PV(1 + r)ᵗ
$2,000 = $1,000(1.12)⁶
$2,000 = $1,000(1.9738)
$2,000 ≈ $1,974 ✓ (close!)

Exam Tips for Practice

• ✅ Show your work - partial credit possible
• ✅ Use correct formulas - write them down first
• ✅ Check units - annual vs. monthly, percentages vs. decimals
• ✅ Round appropriately - usually 2 decimal places for money
• ✅ Label your answers - include units (%, $, years)
• ✅ Double-check calculations - use calculator carefully
• ✅ Read carefully - is it asking for PV or FV? Annual or monthly?

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