Questions: Financial Numeracy and Quantitative Literacy

Question 1

You carry a $3,000 credit card balance at 24% APR and also have $3,000 in savings you could invest at 7% annually. Ignoring minimum payments, which action produces the greater financial benefit over 3 years?

• A. Investing — the stock market builds long-term wealth better than paying off debt
• B. Either choice is roughly equivalent since both involve the same $3,000
• C. Paying off the credit card — the debt compounds at 24% APR, far outpacing a 7% investment return
• D. It depends on whether the stock market outperforms 24% APR in that 3-year window

Answer: (C)

By the Rule of 72, a 24% APR debt doubles in roughly 3 years (72 ÷ 24 = 3), while a 7% investment doubles in roughly 10 years. Paying off the credit card is equivalent to earning a guaranteed 24% return — roughly three times better than the 7% investment. The common mistake is treating all dollar amounts as equivalent; understanding compounding rates reveals the real tradeoff.

Question 2

A financial advisor notes that switching from a fund charging 2% annually to one charging 0.5% annually seems like a trivial 1.5% difference. On a $50,000 portfolio held for 30 years at 6% gross return, roughly how much additional wealth does the lower-fee fund produce?

• A. About $750 — 1.5% of the initial $50,000 invested once
• B. About $2,250 — 1.5% per year × 30 years × initial balance
• C. About $70,000 — the difference between growing at 5.5% vs. 4% over 30 years
• D. About $15,000 — roughly one year of net returns saved

Answer: (C)

$50,000 at 4% (after 2% fee) for 30 years ≈ $162,000; at 5.5% (after 0.5% fee) ≈ $237,000 — a difference of ~$75,000. The 'small' percentage difference compounds relentlessly over decades. This is the core insight of fee sensitivity: framing fees as small percentages obscures their enormous long-term cost.

Question 3

A 24% APR credit card balance that you never pay down will approximately double in 3 years.

• T. True
• F. False

Answer: True

The Rule of 72 states that doubling time ≈ 72 ÷ interest rate. At 24% APR: 72 ÷ 24 = 3 years. This is not intuitive — most people underestimate how fast high-interest debt grows. Internalizing this rule transforms how you evaluate carrying balances: a $5,000 balance could become $10,000 in just 3 years if unpaid.

Question 4

Because percentages are relative, a 2% annual fee on any investment is generally a small cost and can safely be ignored when comparing financial products.

• T. True
• F. False

Answer: False

A 2% annual fee on a $100,000 portfolio is $2,000 per year — money that isn't invested and therefore doesn't compound on your behalf. Over 30 years, this compounds against you, potentially costing hundreds of thousands in lost wealth. Percentage framing obscures absolute dollar costs; converting rates to dollar amounts is the first step in evaluating whether a fee is truly negligible.

Question 5

Why does a small difference in annual investment return (say, 6% vs. 7%) matter far more over 30 years than over 3 years?

Model answer: Because compounding is exponential, not linear. Over 3 years the same rate difference produces a modest gap; over 30 years it compounds repeatedly. At 7%, an investment doubles roughly every 10 years — tripling its doublings over 30 years. At 6%, the doubling period is 12 years, so you complete fewer doublings. Each additional doubling is built on all previous growth, so early rate differences are amplified geometrically over time.

The intuition that 1% doesn't matter comes from linear thinking (1% × 30 = 30%). But compounding works multiplicatively: $10,000 at 7% for 30 years is ~$76,000; at 6% it's ~$57,000 — a $19,000 difference on a $10,000 investment, entirely from one percentage point over time. The longer the horizon, the more each percentage point compounds into real dollars.