Question

how much money would be in an account if $4,000 is deposited at 3% interest compounded continuously and the money is left for 15 years?

Explanation:

Step1: Identify the 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), and \( t\) is the time in years.

Step2: Substitute the values

Given \( P=\$4000\), \( r = 0.03\) (since \( 3\%=0.03\)), and \( t = 15\) years.
Substitute into the formula: \( A=4000\times e^{0.03\times15}\).

Step3: Calculate the exponent

First, calculate \( 0.03\times15 = 0.45\). So the formula becomes \( A = 4000\times e^{0.45}\).

Step4: Evaluate \( e^{0.45}\)

Using a calculator, \( e^{0.45}\approx1.568312\).

Step5: Calculate \( A\)

Multiply \( 4000\times1.568312\approx6273.25\).

Answer:

\( 6273.25\)