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KFind the doubling time of an investment earning 4% interest if interest is compounded continuously.The doubling time of an investment earning 4% interest if interest is compounded continuously is years.(Round to the nearest tenth of a year.)

Respuesta :

Given: An investment earning 4% interest is compounded continuously.

Required: To determine the doubling time of the investment.

Explanation: The formula for continuous compounding is-

[tex]A=Pe^{rt}[/tex]

Here, the amount is doubling. Let $x be invested, then the amount after t years is $2x, and the rate is-

[tex]r=\frac{4}{100}=0.04[/tex]

Substituting the values into the formula as-

[tex]2x=xe^{0.04t}[/tex]

Further simplifying by taking log both sides as-

[tex]\begin{gathered} \ln(2)=0.04t \\ t=17.328 \\ t\approx17.3\text{ years} \end{gathered}[/tex]

Final Answer: The doubling time of an investment earning 4% interest if interest is compounded continuously is 17.3 years.

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