Compound Interest — Practice Quiz

A Financial Math cheat sheet for Compound Interest — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

The future value when interest compounds each period. \(A\) is the future value, \(P\) the principal, \(i = r/n\) the periodic rate, and \(N = nt\) the total number of periods, where \(r\) is the annual rate, \(n\) the compounding periods per year, and \(t\) the years.

$$A = P(1 + i)^{N} \quad\text{or}\quad A = P\left(1 + \dfrac{r}{n}\right)^{nt}$$

The principal (present value) needed today to reach a future value \(A\) with compounding, where \(i = r/n\) is the periodic rate and \(N = nt\) the total number of periods.

$$P = \dfrac{A}{(1 + i)^{N}} \quad\text{or}\quad P = \dfrac{A}{\left(1 + \frac{r}{n}\right)^{nt}}$$

The future value under continuous compounding, using \(e \approx 2.718\). \(P\) is the principal, \(r\) the annual rate, and \(t\) the time in years.

$$A = Pe^{rt}$$

Practice quiz

  1. You invest \$5,000 in an account that pays $4\%$ annual interest compounded annually. What will be the value of your investment after $10$ years? Round to the nearest cent.

    • \$7,401.22
    • \$7,000.00
    • \$7,454.16
    • \$5,200.00

    Answer: \$7,401.22

  2. A principal of \$10,000 is invested at an annual interest rate of $6\%$ compounded monthly. What will be the future value after $5$ years? Round to the nearest cent.

    • \$13,488.50
    • \$13,382.26
    • \$13,000.00
    • \$10,616.78

    Answer: \$13,488.50

  3. How much money must be deposited today in an account paying $3\%$ annual interest compounded quarterly to have \$20,000 in $8$ years? Round to the nearest cent.

    • \$15,746.65
    • \$25,402.22
    • \$15,788.18
    • \$16,129.03

    Answer: \$15,746.65

  4. If \$7,500 is invested at an annual interest rate of $5\%$ compounded continuously, what will be the value of the investment after $6$ years? Round to the nearest cent.

    • \$10,123.94
    • \$9,750.00
    • \$10,050.72
    • \$10,117.63

    Answer: \$10,123.94

  5. You have \$1,000 to invest for $3$ years. Option A offers $4\%$ annual interest compounded semi-annually. Option B offers $3.95\%$ annual interest compounded monthly. Which option yields a higher future value, and by how much? Round to the nearest cent.

    • Option A by \$0.57
    • Option B by \$-0.57
    • Option A by \$1,126.16
    • Option B by \$1,125.59

    Answer: Option A by \$0.57

  6. For an investment with an annual interest rate $r$ compounded $n$ times per year over $t$ years, what are the correct expressions for the periodic interest rate $i$ and the total number of compounding periods $N$?

    • $i = r/n$, $N = nt$
    • $i = r$, $N = t$
    • $i = r \cdot n$, $N = t/n$
    • $i = r/t$, $N = n$

    Answer: $i = r/n$, $N = nt$

  7. What principal amount must be invested today at an annual interest rate of $4.5\%$ compounded continuously to reach a future value of \$15,000 in $7$ years? Round to the nearest cent.

    • \$10,946.83
    • \$20,553.89
    • \$11,022.43
    • \$11,406.84

    Answer: \$10,946.83

  8. An initial deposit of \$2,500 is made into an account that pays $2.5\%$ annual interest compounded daily. What will be the account balance after $2$ years? Assume $365$ days in a year and round to the nearest cent.

    • \$2,628.17
    • \$2,628.04
    • \$2,626.56
    • \$2,625.00

    Answer: \$2,628.17

  9. You invest \$8,000 at an annual interest rate of $3.5\%$ compounded semi-annually. How much will your investment be worth after $15$ years? Round to the nearest cent.

    • \$13,462.40
    • \$13,402.79
    • \$13,492.82
    • \$12,200.00

    Answer: \$13,462.40

  10. An investment of \$12,000 is made for $10$ years at an annual interest rate of $5\%$. How much more interest is earned if the interest is compounded continuously compared to being compounded annually? Round to the nearest cent.

    • \$237.92
    • \$-237.92
    • \$19,784.66
    • \$19,546.74

    Answer: \$237.92

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