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A person places $419 in an investment account earning an annual rate of 9.2%, compounded continuously. Using the formula V=PertV=Pe rt, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 20 years.

Respuesta :

Answer:

[tex]V=\$2638.25[/tex]

Step-by-step explanation:

From the given information

Principal Initially Invested, P =$419

Annual Rate, r=9.2% =0,092

Time, t = 20 Years

Since it is compounded continuously, the value after t years is determined using the given model:

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

Substituting the given values

[tex]V=419*e^{0.092*20}\\V=\$2638.25[/tex]

The value of the account after 20 years is [tex]V=\$2638.25[/tex] (correct to the nearest cent)

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