hadley has decided to invest some money in a bank that offers continuous compounding interest. use the…

hadley has decided to invest some money in a bank that offers continuous compounding interest. use the formula to determine the value of hadleys investment after 3 years.\n$a = pe^{rt}$\nprincipal amount ($p$): $3,000\nannual interest rate ($r$): 3.5% or 0.035\ntime ($t$): 3 years\nenter your answer in the box, rounding to two decimal places.

hadley has decided to invest some money in a bank that offers continuous compounding interest. use the formula to determine the value of hadleys investment after 3 years.\n$a = pe^{rt}$\nprincipal amount ($p$): $3,000\nannual interest rate ($r$): 3.5% or 0.035\ntime ($t$): 3 years\nenter your answer in the box, rounding to two decimal places.

Answer

Explanation:

Step1: Substitute the values into the formula

Given (P = 3000), (r=0.035), (t = 3), and the formula (A=Pe^{rt}). Substitute these values: (A = 3000\times e^{0.035\times3}).

Step2: Calculate the exponent

First, calculate (0.035\times3=0.105). So the formula becomes (A = 3000\times e^{0.105}).

Step3: Find the value of (e^{0.105})

Using a calculator, (e^{0.105}\approx1.1107106).

Step4: Calculate the final amount

Multiply (3000) by (1.1107106): (A=3000\times1.1107106 = 3332.1318).

Step5: Round to two decimal places

Rounding (3332.1318) to two decimal places gives (3332.13).

Answer:

(3332.13)