lia has opened a new savings account with an interest rate that compounds continuously. calculate the amount…

lia has opened a new savings account with an interest rate that compounds continuously. calculate the amount she will have after the specified time.\n$a = pe^{rt}$\nprincipal amount ($p$): $2,500\nannual interest rate ($r$): $4.2%$ or $0.042$\ntime ($t$): $5$ years\nenter your answer in the box, rounding to two decimal places.\n$

lia has opened a new savings account with an interest rate that compounds continuously. calculate the amount she will have after the specified time.\n$a = pe^{rt}$\nprincipal amount ($p$): $2,500\nannual interest rate ($r$): $4.2%$ or $0.042$\ntime ($t$): $5$ years\nenter your answer in the box, rounding to two decimal places.\n$

Answer

Explanation:

Step1: Substitute values into formula

Substitute (P = 2500), (r=0.042), and (t = 5) into (A=Pe^{rt}). [A = 2500\times e^{0.042\times5}]

Step2: Calculate exponent

First calculate (0.042\times5=0.21). [A = 2500\times e^{0.21}]

Step3: Evaluate (e^{0.21})

Using a calculator, (e^{0.21}\approx1.233678). [A = 2500\times1.233678]

Step4: Multiply

(2500\times1.233678 = 3084.195)

Step5: Round to two decimal places

Rounding (3084.195) to two decimal places gives (3084.20).

Answer:

(3084.20)