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Continuous Compound Interest Practice Problems

Every problem here uses one formula, A = Pe^(rt), sometimes forwards and sometimes backwards with a natural log. The first four warm up the formula, the middle four add the effective rate, doubling time and present value, and the last four make you solve for the exponent.

  1. 1.

    An account pays 3.5% interest compounded continuously. What value of goes into ?

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    Divide the percentage by 100: .

  2. 2.

    $1,000 is invested at 5% compounded continuously. What is the balance after 1 year, in dollars?

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    .

  3. 3.

    What is the growth factor for 6% compounded continuously over 10 years, to four decimal places?

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    , and . Every dollar becomes about $1.82.

  4. 4.

    How much interest does $2,000 earn in 5 years at 3% compounded continuously, in dollars?

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    , so the interest is .

  5. 5.

    $7,500 is invested at 4.2% compounded continuously. What is it worth after 8 years, in dollars?

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    , so .

  6. 6.

    What is the effective annual rate of 7% compounded continuously, as a percentage to two decimal places?

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    , or about .

  7. 7.

    How many years does it take money to double at 8% compounded continuously? Give two decimal places.

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    Set , so years.

  8. 8.

    How much must you invest now at 5% compounded continuously to have $15,000 in 6 years, in dollars?

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    .

  9. 9.

    How many years will it take $4,000 to grow to $10,000 at 6% compounded continuously? Give two decimal places.

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    , so years.

  10. 10.

    An investment compounded continuously grew from $2,500 to $4,000 in 9 years. What was the annual rate, as a percentage to two decimal places?

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    , so , about .

  11. 11.

    How many years does it take money to triple at 4.5% compounded continuously? Give two decimal places.

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    , so years.

  12. 12.

    $10,000 is invested at 6% for 20 years. How many more dollars does continuous compounding earn than monthly compounding?

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    Continuous: . Monthly: . The difference is about , roughly 0.3% after twenty years.
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MPhil in Mathematics, Founder of Mathovia
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Continuous Compound Interest Practice Problems

These problems follow the continuous compound interest lesson. If the natural log steps feel shaky, the common and natural logarithms lesson covers them.

The formulas you need

To findFormula
final amount
interest earned
principal (present value)
time
rate
doubling time
effective annual rate

Before you calculate

Turn the percentage into a decimal first, since 5% is . Keep in years, so 18 months is . Leave unrounded on your calculator and round only the final answer.

Common mistakes to watch for

  • Using the rate as a percentage. In , 5% is .
  • Mixing time units. must be in years if is an annual rate.
  • Using the periodic formula. Continuous compounding uses , not .
  • Solving for time without logs. Isolate , then take of both sides.

Frequently Asked Questions

What formula do I use for continuous compound interest problems?+

A = Pe^(rt), with P the principal, r the annual rate as a decimal and t the time in years. To find time or rate, divide by P and take the natural log: t = ln(A/P) / r and r = ln(A/P) / t.

How do I find the doubling time quickly?+

Divide ln 2 ≈ 0.693 by the rate as a decimal. At 8% that is 0.693 / 0.08 ≈ 8.66 years. With the rate as a percentage, divide 69.3 by it.

What is the effective annual rate for continuous compounding?+

EAR = e^r − 1. It is the once-a-year rate that gives the same growth, so 7% compounded continuously is the same as about 7.25% compounded annually.

How should I enter money answers?+

Type the number without commas, for example 10495.04. A dollar sign and the comma-formatted version are also accepted, and answers within a cent are marked correct.

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