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.

Practice quiz

1. An investment grows at a $CAGR$ of $10\%$ for $5$ years. What is the total $ROI$ over this period, expressed as a percentage to two decimal places?

   • $50.00\%$
   • $61.05\%$
   • $72.89\%$
   • $100.00\%$

   Answer: $61.05\%$

2. An investment yields a total $ROI$ of $75\%$ over $7$ years. What is the equivalent $CAGR$ for this investment, expressed as a percentage to two decimal places?

   • $7.50\%$
   • $8.39\%$
   • $9.17\%$
   • $10.71\%$

   Answer: $8.39\%$

3. Consider two investments, A and B. Investment A has a $CAGR$ of $8\%$ over $10$ years. Investment B has a total $ROI$ of $100\%$ over $5$ years. Which statement is true regarding their annualized growth rates and total returns?

   • Investment A has a higher $CAGR$ and a higher total $ROI$.
   • Investment B has a higher $CAGR$, but Investment A has a higher total $ROI$.
   • Investment A has a higher $CAGR$, but Investment B has a higher total $ROI$.
   • Investment B has a higher $CAGR$ and a higher total $ROI$.

   Answer: Investment B has a higher $CAGR$, but Investment A has a higher total $ROI$.

4. Given the $CAGR$ formula, $CAGR = \left(\frac{FV}{PV}\right)^{\frac{1}{t}} - 1$, derive an expression for $t$ in terms of $FV$, $PV$, and $CAGR$.

   • $t = \frac{\ln(FV) - \ln(PV)}{\ln(1 + CAGR)}$
   • $t = \frac{\ln(1 + CAGR)}{\ln(FV) - \ln(PV)}$
   • $t = \frac{\ln(FV/PV)}{1 + CAGR}$
   • $t = \frac{\ln(FV) + \ln(PV)}{\ln(1 + CAGR)}$

   Answer: $t = \frac{\ln(FV) - \ln(PV)}{\ln(1 + CAGR)}$

5. Given an investment's $ROI$ (as a decimal) and its $FV$, derive an expression for $PV$.

   • $PV = FV \times (1 + ROI)$
   • $PV = \frac{FV}{1 - ROI}$
   • $PV = \frac{FV}{1 + ROI}$
   • $PV = FV - ROI$

   Answer: $PV = \frac{FV}{1 + ROI}$

6. An investor puts $\$10,000$ into Investment X, which promises a $CAGR$ of $7\%$ for $10$ years. Simultaneously, another investor puts $\$10,000$ into Investment Y, which guarantees a total $ROI$ of $100\%$ over $8$ years. Which investment yields a higher final value, and by approximately how much?

   • Investment X by approximately $\$328.50$
   • Investment Y by approximately $\$328.50$
   • Investment X by approximately $\$1,000.00$
   • Investment Y by approximately $\$1,000.00$

   Answer: Investment Y by approximately $\$328.50$

7. An initial investment of $\$5,000$ grows with a $CAGR$ of $12\%$ for $3$ years. At the end of the third year, the accumulated value is reinvested for another $2$ years, achieving an additional $ROI$ of $25\%$ over these $2$ years. What is the overall $ROI$ of the entire $5$-year period, expressed as a percentage to two decimal places?

   • $65.24\%$
   • $70.00\%$
   • $75.62\%$
   • $82.15\%$

   Answer: $75.62\%$

8. If an investment's $PV$ is doubled, but its $FV$ remains unchanged, how does the $ROI$ change?

   • The $ROI$ is halved.
   • The $ROI$ is doubled.
   • The $ROI$ decreases, potentially becoming negative.
   • The $ROI$ remains the same.

   Answer: The $ROI$ decreases, potentially becoming negative.

9. An investor aims for a total $ROI$ of $150\%$ over $6$ years. What $CAGR$ must the investment achieve to meet this target, expressed as a percentage to two decimal places?

   • $12.25\%$
   • $14.87\%$
   • $16.65\%$
   • $18.03\%$

   Answer: $16.65\%$

10. An investment of $\$20,000$ is made for $4$ years. If the investment achieves a $CAGR$ of $15\%$, what is the total $ROI$ and the final $FV$?

    • Total $ROI = 60.00\%$, $FV = \$32,000.00$
    • Total $ROI = 74.90\%$, $FV = \$34,980.13$
    • Total $ROI = 74.90\%$, $FV = \$34,000.00$
    • Total $ROI = 60.00\%$, $FV = \$34,980.13$

    Answer: Total $ROI = 74.90\%$, $FV = \$34,980.13$