Question

multiple choice 1 point
steve invests $1,800 in an account that earns 3.7% annual interest, compounded continuously.
what is the approximate value of the account after 10 years?
$2,466
$2,589
$2,601
$2,606

Explanation:

Step1: Recall the continuous - compounding formula

The formula for continuous compounding is \(A = Pe^{rt}\), where \(P\) is the principal amount, \(r\) is the annual interest rate (in decimal form), \(t\) is the time in years, and \(e\approx2.71828\).
Given \(P = 1800\), \(r=0.037\), and \(t = 10\).

Step2: Substitute the values into the formula

Substitute \(P = 1800\), \(r = 0.037\), and \(t=10\) into \(A=Pe^{rt}\).
We get \(A = 1800\times e^{0.037\times10}=1800\times e^{0.37}\).

Step3: Calculate \(e^{0.37}\)

Using a calculator, \(e^{0.37}\approx1.4477\).

Step4: Calculate the value of \(A\)

Then \(A=1800\times1.4477 = 2605.86\approx2606\).

Answer:

\(\$2606\)