Question

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.
$a = pe^{rt}$
principal amount ($p$): $3,000
annual interest rate ($r$): 3.5% or 0.035
time ($t$): 3 years
enter your answer in the box, rounding to two decimal places.

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:

\(3332.13\)