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. An initial investment of $1000$ is made into an account that pays $5\%$ annual interest, compounded annually. What will be the future value of the investment after $10$ years?

    • $\$1500.00$
    • $\$1628.89$
    • $\$1600.00$
    • $\$1647.01$

    Answer: $\$1628.89$

  2. You deposit $5000$ into a savings account that offers an annual interest rate of $4\%$ compounded quarterly. What will be the balance in the account after $5$ years?

    • $\$6000.00$
    • $\$6100.96$
    • $\$6083.26$
    • $\$6104.08$

    Answer: $\$6100.96$

  3. What principal amount must be invested today to have $10000$ in $3$ years, if the interest rate is $6\%$ compounded monthly?

    • $\$8356.45$
    • $\$8400.00$
    • $\$8333.33$
    • $\$8374.84$

    Answer: $\$8356.45$

  4. Calculate the future value of $2000$ invested for $7$ years at an annual interest rate of $3\%$ compounded continuously.

    • $\$2420.00$
    • $\$2467.34$
    • $\$2450.00$
    • $\$2472.12$

    Answer: $\$2467.34$

  5. Which of the following investment options would yield the highest future value for an initial principal of $1000$ over $1$ year?

    • A) $5\%$ annual interest compounded annually
    • B) $4.95\%$ annual interest compounded semi-annually
    • C) $4.9\%$ annual interest compounded monthly
    • D) $4.85\%$ annual interest compounded continuously

    Answer: B) $4.95\%$ annual interest compounded semi-annually

  6. In the formula $A = P(1 + i)^{N}$, what does the variable $N$ represent?

    • The annual interest rate
    • The number of years the money is invested
    • The total number of compounding periods
    • The number of times interest is compounded per year

    Answer: The total number of compounding periods

  7. All else being equal, how does increasing the number of compounding periods per year ($n$) affect the future value ($A$) of an investment?

    • It decreases $A$
    • It increases $A$
    • It has no effect on $A$
    • It only affects $A$ if the interest rate is very high

    Answer: It increases $A$

  8. You want to have $15000$ in $4$ years for a down payment on a car. If you can invest your money at an annual rate of $3.5\%$ compounded semi-annually, how much should you invest today?

    • $\$13060.70$
    • $\$13100.00$
    • $\$13000.00$
    • $\$13125.00$

    Answer: $\$13060.70$

  9. Which compounding frequency will result in the highest future value for a given principal, annual interest rate, and time period?

    • Annually
    • Quarterly
    • Monthly
    • Continuously

    Answer: Continuously

  10. An investor deposits $2000$ into an account earning $4\%$ interest compounded quarterly. After $3$ years, an additional $1000$ is deposited into the same account. What will be the total value of the investment after $5$ years from the initial deposit?

    • $\$3750.00$
    • $\$3834.00$
    • $\$3800.00$
    • $\$3852.15$

    Answer: $\$3834.00$

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