How long will it take money to double if it is invested at 4% compounded continuously?

There are several ways to do this problem. The easiest way to solve it is to take the ln(2) and divide it by the interest rate. For this problem, assuming that your rates are annual, this formula gives us ln(2)/.13 = 5.33 years and ln(2)/.15 = 4.62 years.

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Compound Interest Curve
Practice using the Rule of 72
Why Stop at a Double?
Why Does the Rule of 72 Work?
How long will it take money to double if it is in…
Problem 25 Easy Difficulty
Watch More Solved Questions in Chapter 4
Video Transcript
How long would it take for your money to double if it is invested at 4% compounded continuously?
How long will it take to double your money at a 4% interest rate?
How do you calculate compounded continuously doubling time?
How long will it take money to double if it is invested at 5% compounded continuously?

Why does this work? We know that the continuous compounding formula is A = Pe^(rt). Therefore, we can solve this equation to indicate doubling your investment like so: 2 = 1e^(rt). For the first question, we can then plug in our rate of 13%. This would give us 2 = e^(.13t). In order to solve for t, we would take the ln of both sides of the equation (ln 2 = ln e^(.13t)), which would then simplify to ln 2 = .13t. Therefore, we are back to our original equation, which is ln 2 / r = t.

Have you always wanted to be able to do compound interest problems in your head? Perhaps not... but it's a very useful skill to have because it gives you a lightning fast benchmark to determine how good (or not so good) a potential investment is likely to be.

The rule says that to find the number of years required to double your money at a given interest rate, you just divide the interest rate into 72. For example, if you want to know how long it will take to double your money at eight percent interest, divide 8 into 72 and get 9 years.

Y = 72 / r and r = 72 / Y
where Y and r are the years and interest rate, respectively.

Compound Interest Curve

Suppose you invest $100 at a compound interest rate of 10%. The rule of 72 tells you that your money will double every seven years, approximately:

Years	Balance
Now	$100
7	$200	(doubles every
14	$400	seven years)
21	$800

If you graph these points, you start to see the familiar compound interest curve:

Practice using the Rule of 72

It's good to practice with the rule of 72 to get an intuitive feeling for the way compound interest works. So...

Why Stop at a Double?

There's nothing sacred about doubling your money. You can also get a simple estimate for other growth factors, as this calculator shows:

Why Does the Rule of 72 Work?

If you want to know more, see this explanation of why the rule of 72 works. (Brace yourself, because it's slightly geeked out.)

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Problem 25 Easy Difficulty

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The Constant e and Continuous Compound Interest

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Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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Differentiation Rules - Example 1

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Calculus for Business, Economics, Life Sciences and Social Sciences

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How long would it take for your money to double if it is invested at 4% compounded continuously?

If the interest per quarter is 4% (but interest is only compounded annually), then it will take (72 / 4) = 18 quarters or 4.5 years to double the principal. If the population of a nation increases at the rate of 1% per month, it will double in 72 months, or six years.

How long will it take to double your money at a 4% interest rate?

If, for example, your account earns 4 percent, divide 72 by 4 to get the number of years it will take for your money to double. In this case, 18 years.

How do you calculate compounded continuously doubling time?

When interest is compounded a given number of times per year use the formula A(t)=P(1+rn)nt. When interest is to be compounded continuously use the formula A(t)=Pert. Doubling time is the period of time it takes a given amount to double.

How long will it take money to double if it is invested at 5% compounded continuously?

Yearly rate of compound interest = 5%. Quarterly rate of compound interest = (5 / 4)%. Thus, after 56 quarters, that is, after 14 years the amount will get doubled.