a person places $8440 in an investment account earning an annual rate of 9.2%, compounded continuously…

a person places $8440 in an investment account earning an annual rate of 9.2%, compounded continuously. using the formula $v = pe^{rt}$, 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 8 years.

a person places $8440 in an investment account earning an annual rate of 9.2%, compounded continuously. using the formula $v = pe^{rt}$, 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 8 years.

Answer

Explanation:

Step1: Identify the values

$P = 8440$, $r=0.092$, $t = 8$

Step2: Substitute values into formula

$V=Pe^{rt}=8440\times e^{0.092\times8}$

Step3: Calculate the exponent

$0.092\times8 = 0.736$

Step4: Calculate the value of $e^{0.736}$

Using a calculator, $e^{0.736}\approx2.08797$

Step5: Calculate the final value

$V = 8440\times2.08797\approx17622.57$

Answer:

$17622.57$