Market & Investment Performance — Hard Practice Quiz

A Financial Math cheat sheet for Market & Investment Performance — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Formulas & key concepts

Return on investment: the percentage gain or loss on an investment. \(FV\) is the ending value and \(PV\) the initial amount invested.

$$ROI = \dfrac{FV - PV}{PV} \times 100\%$$

The compound annual growth rate, the constant yearly rate at which an investment would have grown from \(PV\) to \(FV\) over \(t\) years.

$$CAGR = \left(\dfrac{FV}{PV}\right)^{\frac{1}{t}} - 1$$

Practice quiz

  1. An initial investment of \$10,000 grows at a compound annual growth rate (CAGR) of $8.5\%$ for $7$ years. What is the return on investment (ROI) over this period? Round your answer to two decimal places.

    • $77.01\%$
    • $59.50\%$
    • $0.77\%$
    • $84.72\%$

    Answer: $77.01\%$

  2. An investment of \$25,000 yielded a total return on investment (ROI) of $60\%$ over a period of $5$ years. What was the compound annual growth rate (CAGR) for this investment? Round your answer to four decimal places.

    • $9.8561\%$
    • $12.0000\%$
    • $948.5760\%$
    • $109.8561\%$

    Answer: $9.8561\%$

  3. For an investment held for exactly one year, how does the return on investment (ROI) relate to the compound annual growth rate (CAGR)?

    • $ROI = CAGR \times 100\%$
    • $ROI = CAGR$
    • $ROI = CAGR + 1$
    • $ROI = \frac{CAGR}{100\%}$

    Answer: $ROI = CAGR \times 100\%$

  4. An investor aims to have \$50,000 in $10$ years. If they expect an annual compound growth rate (CAGR) of $6\%$, what initial principal value (PV) must they invest today? Round to the nearest cent.

    • \$27,919.74
    • \$31,250.00
    • \$49,709.50
    • \$89,542.38

    Answer: \$27,919.74

  5. An investment of \$15,000 grew to \$30,000 with a compound annual growth rate (CAGR) of $7.2\%$. Approximately how many years did it take for the investment to reach this final value? Round to two decimal places.

    • $9.97$ years
    • $13.89$ years
    • $0.05$ years
    • $0.10$ years

    Answer: $9.97$ years

  6. If an investment's initial principal value ($PV$) is doubled, but its final value ($FV$) remains unchanged, how does the return on investment ($ROI$) change?

    • It decreases, but not necessarily by half.
    • It doubles.
    • It halves.
    • It increases.

    Answer: It decreases, but not necessarily by half.

  7. An investment of \$5,000 grew at a CAGR of $10\%$ for the first $3$ years. After these $3$ years, the accumulated value then grew at a CAGR of $7\%$ for an additional $2$ years. What is the total return on investment (ROI) over the entire $5$-year period? Round to two decimal places.

    • $52.39\%$
    • $44.00\%$
    • $50.37\%$
    • $51.73\%$

    Answer: $52.39\%$

  8. An investment achieved a total return on investment (ROI) of $120\%$ over $8$ years. What was the equivalent compound annual growth rate (CAGR) for this investment? Round to four decimal places.

    • $10.3577\%$
    • $15.0000\%$
    • $110.3577\%$
    • $54{,}775.8735\%$

    Answer: $10.3577\%$

  9. Investment A started with \$12,000 and grew to \$20,000 in $4$ years. Investment B started with \$15,000 and achieved a CAGR of $9\%$ over $5$ years. What is the difference in their total return on investment (ROI), specifically $ROI_B - ROI_A$? Round to two decimal places.

    • $-12.80\%$
    • $12.80\%$
    • $-21.67\%$
    • $-0.05\%$

    Answer: $-12.80\%$

  10. An investment of \$10,000 achieved a total return on investment (ROI) of $75\%$ over $6$ years. If the compound annual growth rate (CAGR) for the first $3$ years was $12\%$, what was the CAGR for the remaining $3$ years? Round to four decimal places.

    • $7.5956\%$
    • $8.7676\%$
    • $93.2644\%$
    • $7.5515\%$

    Answer: $7.5956\%$

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