Question

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.)

Answer 1

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-

`A=Pe^(rt)`

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

`r=(4)/(100)=0.04`

Substituting the values into the formula as-

`2x=xe^(0.04t)`

Further simplifying by taking log both sides as-

`\begin{gathered} \ln(2)=0.04t \\ t=17.328 \\ t\approx17.3\text{ years} \end{gathered}`

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

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