a person places $913 in an investment account earning an annual rate of 5.7%, compounded continuously. using…

a person places $913 in an investment account earning an annual rate of 5.7%, 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 20 years.

a person places $913 in an investment account earning an annual rate of 5.7%, 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 20 years.

Answer

Explanation:

Step1: Identify the values

$P = 913$, $r=0.057$, $t = 20$

Step2: Substitute into the formula

$V=Pe^{rt}=913\times e^{0.057\times20}$

Step3: Calculate the exponent

$0.057\times20 = 1.14$

Step4: Calculate $e^{1.14}$

Using a calculator, $e^{1.14}\approx3.126767$

Step5: Calculate the final value

$V = 913\times3.126767\approx2854.74$

Answer:

$2854.74$