Question

ivana has decided to invest some money in a bank that offers continuous compounding interest. how much will be in the account after 10 years?
a = pe^{rt}
principal amount (p): $1,000
annual interest rate (r): 5% or 0.05
time (t): 10 years
enter your answer in the box, rounding to two decimal places.
$

Explanation:

Step1: Substitute values into formula

Given \(A = Pe^{rt}\), \(P=\$1000\), \(r = 0.05\), \(t = 10\). Substitute into the formula: \(A=1000\times e^{0.05\times10}\).

Step2: Calculate the exponent

First calculate \(0.05\times10 = 0.5\). So the formula becomes \(A = 1000\times e^{0.5}\).

Step3: Evaluate \(e^{0.5}\)

Using a calculator, \(e^{0.5}\approx1.64872\).

Step4: Calculate \(A\)

Multiply \(1000\times1.64872 = 1648.72\).

Answer:

\(1648.72\)