how much money would be in an account if $4,000 is deposited at 3% interest compounded continuously and the…

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)