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Suppose an investment earns 3.4%
interest compounded continuously. How long will it take an investment of $3000
to be worth $4000
? Round your answer to the nearest hundredth.

Sagot :

Sqdancefanidn

Answer:

  8.46 years

Step-by-step explanation:

You want to know how long it takes for an investment of $3000 earning 3.4% interest compounded continuously to have a value of $4000.

Value

The value of the investment P earning rate r for t years is ...

  [tex]A=Pe^{rt}[/tex]

Solving for t, we find ...

  [tex]\dfrac{A}{P}=e^{rt}\\\\t=\dfrac{\ln(\dfrac{A}{P})}{r}=\dfrac{\ln(\dfrac{4000}{3000})}{0.034}\approx8.46[/tex]

It will take about 8.46 years for the investment to be worth $4000.

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