Big Numbers in the Economy: Estimate GDP, Inflation Math, and Compound Interest

63 questions · by Quizbun

Sixty-three questions that turn the economy's most quoted numbers into math you can actually do in your head. Three pillars: estimating GDP (the C + I + G + (X − M) identity, real vs. nominal, the GDP deflator, per-capita arithmetic, and the famous 2023 figures), inflation math (reading the CPI, the Rule of 70, real interest rates, and what hyperinflation really means), and compound interest (the Rule of 72, doubling time, CAGR, APR vs. APY, and continuous compounding with e). Most answers are numeric so you practice the calculation, not just recognition. Every explanation is followed by a Wikipedia or primary-source reference (BEA or the Federal Reserve) so you can verify the figure and read further — and a few questions deliberately debunk a popular but false 'fact'.

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Questions

Not answered. On the short scale used in the US and modern UK, how many zeros does one trillion have when written out as 1 followed by zeros?
Not answered. On the short scale, one billion equals how many millions?
Not answered. Roughly how many years is one billion seconds?
Not answered. What does Gross Domestic Product (GDP) measure?
Not answered. Which equation is the standard expenditure formula for GDP?
Not answered. In GDP = C + I + G + (X − M), what does the (X − M) term represent?
Not answered. GDP can be measured three different ways that should, in principle, give the same total. Which are they?
Not answered. Which of the following are generally excluded from a country's GDP?
Not answered. What is the difference between nominal GDP and real GDP?
Not answered. What is the formula for the GDP deflator?
Not answered. If nominal GDP is $120 billion and the GDP deflator is 120 (base-year = 100), what is real GDP, in billions of dollars?
Not answered. What does GDP per capita tell you?
Not answered. An economy produces $24 trillion of GDP for a population of 300 million people. What is GDP per capita, in thousands of dollars?
Not answered. Approximately what was the nominal GDP of the United States in 2023, in trillions of US dollars?
Not answered. Approximately, what was total world GDP (nominal) in 2023, in trillions of US dollars?
Not answered. Which had the world's largest nominal GDP in 2023?
Not answered. In 2023, which country became the world's third-largest economy by nominal GDP, overtaking Japan?
Not answered. Why can a country's PPP GDP differ a lot from its nominal (market-exchange-rate) GDP?
Not answered. What is the key difference between GDP and GNP (now usually called GNI)?
Not answered. If nominal GDP grew 5% over a year while inflation (the GDP deflator) rose 2%, approximately what was real GDP growth, in percent?
Not answered. What is the common journalistic rule of thumb for a recession?
Not answered. What does a country's debt-to-GDP ratio express?
Not answered. By the early 2020s, US gross federal debt was approximately what fraction of GDP?
Not answered. What is inflation?
Not answered. What does the Consumer Price Index (CPI) measure?
Not answered. If a price index rises from 200 to 210 over one year, what is the inflation rate, in percent?
Not answered. After a cumulative 25% rise in prices, what is the real purchasing power of $100, expressed in original dollars?
Not answered. Using the Rule of 70, about how many years does it take for prices to double at a steady 7% annual inflation?
Not answered. At a steady 3.5% annual inflation, prices double in roughly how many years (Rule of 70)?
Not answered. What annual inflation rate does the US Federal Reserve target over the longer run?
Not answered. In which year did the US Federal Reserve first formally announce its explicit 2% inflation target?
Not answered. What is deflation?
Not answered. Inflation falls from 6% last year to 3% this year, but prices are still rising. What is this called?
Not answered. What does stagflation describe?
Not answered. By the classic definition (Phillip Cagan, 1956), an episode becomes hyperinflation once the inflation rate exceeds what, per month?
Not answered. Cagan's threshold of 50% inflation per month, compounded for a year, comes to approximately what annual rate?
Not answered. Which country suffered the worst hyperinflation ever recorded, with prices doubling about every 15 hours?
Not answered. At the November 2008 peak of Zimbabwe's hyperinflation, prices roughly doubled how often?
Not answered. What is the difference between a nominal and a real interest rate?
Not answered. A bond pays a 6% nominal interest rate and inflation is 2%. Approximately what is the real interest rate, in percent?
Not answered. Which is the exact Fisher equation relating the nominal rate i, real rate r, and inflation π?
Not answered. What does the equation of exchange, M × V = P × Q, relate?
Not answered. In M × V = P × Q, what is the velocity of money V?
Not answered. Which is the standard compound interest formula for a final amount A?
Not answered. How does compound interest differ from simple interest?
Not answered. How much total interest does $1,000 earn at 10% simple interest over 3 years, in dollars?
Not answered. What does $1,000 grow to at 5% interest compounded annually over 10 years? Give the amount to the nearest dollar.
Not answered. What does the Rule of 72 let you estimate?
Not answered. Using the Rule of 72, how many years does it take to double your money at a 6% annual return?
Not answered. Using the Rule of 72, what annual return (in percent) is needed to double your money in 9 years?
Not answered. Around what interest rate is the Rule of 72 most accurate?
Not answered. Which statements about the Rule of 72 and its cousins are correct?
Not answered. What is the exact formula for the time t it takes a quantity growing at rate r per period to double?
Not answered. The Rule of 69.3 comes from the natural logarithm of 2. What is ln(2), to three decimal places?
Not answered. Which formula gives the future value under continuous compounding?
Not answered. $1 invested at a 100% annual rate, compounded continuously for one year, grows to what value? (This limit defines Euler's number.)
Not answered. What is the difference between APR (annual percentage rate) and APY (annual percentage yield)?
Not answered. A 12% APR is compounded monthly. What is the APY (effective annual yield), in percent, to two decimals?
Not answered. What does CAGR (compound annual growth rate) measure?
Not answered. An investment grows from $100 to $200 over 6 years. What is its CAGR, in percent, to one decimal?
Not answered. What is the present value of a future sum of money?
Not answered. At a 10% discount rate, what is the present value of $1,331 received 3 years from now, in dollars?
Not answered. A popular quote calls compound interest 'the eighth wonder of the world,' usually attributed to Albert Einstein. Is that attribution real?