gary wants to save money for a new car using a high - yield account that offers continuous compounding…

gary wants to save money for a new car using a high - yield account that offers continuous compounding interest. how much will be in garys account after 4 years?\n$a = pe^{rt}$\nprincipal amount $(p): $4,500$\nannual interest rate $(r): 3.8%$ or $0.038$\ntime $(t): 4$ years\nenter your answer in the box, rounding to two decimal places.

gary wants to save money for a new car using a high - yield account that offers continuous compounding interest. how much will be in garys account after 4 years?\n$a = pe^{rt}$\nprincipal amount $(p): $4,500$\nannual interest rate $(r): 3.8%$ or $0.038$\ntime $(t): 4$ years\nenter your answer in the box, rounding to two decimal places.

Answer

Explanation:

Step1: Identify values

$P = 4500$, $r=0.038$, $t = 4$

Step2: Substitute into formula

$A=4500\times e^{0.038\times4}$

Step3: Calculate exponent

$0.038\times4 = 0.152$

Step4: Calculate $e^{0.152}$

Using a calculator, $e^{0.152}\approx1.16493$

Step5: Calculate final amount

$A = 4500\times1.16493=5242.185$

Step6: Round to two decimal places

$A\approx5242.19$

Answer:

$5242.19$