Question

part 1 of 2
jae invested $3,500 at a rate of 2.25% compounded continuously in 2010. how much will be in the account in 2025? how much interest will the account have earned by 2025?
there will be $□ in the account in 2025.
(round to the nearest cent as needed.)

Explanation:

Step1: Define variables for formula

$P = 3500$, $r = 0.0225$, $t = 2025-2010=15$

Step2: Apply continuous compound formula

$A = Pe^{rt} = 3500e^{0.0225\times15}$

Step3: Calculate exponent term

$0.0225\times15 = 0.3375$, so $e^{0.3375}\approx1.378294$

Step4: Compute total account value

$A = 3500\times1.378294\approx4824.03$

Step5: Calculate earned interest

$I = A-P = 4824.03-3500=1274.03$

Answer:

There will be $\$4,824.03$ in the account in 2025.
The account will have earned $\$1,274.03$ in interest by 2025.