Question

1. maria leaves $5000 in the bank for 15 years. it earns compound interest of 3.6% compounded continuously. write the equation and calculate the total amount maria has in the bank at the end of the 15 years.

p = _____________ r = ___________ t = _____________
equation: _______________________ balance in 15 years: $_______________________

Explanation:

Step1: Identify given values

$P = 5000$, $r = 0.036$, $t = 15$

Step2: Recall continuous compound formula

The formula for continuous compound interest is $A = Pe^{rt}$, where $A$ is the final amount.

Step3: Substitute values into formula

$A = 5000e^{0.036 \times 15}$

Step4: Calculate exponent term

$0.036 \times 15 = 0.54$

Step5: Compute exponential and final amount

$e^{0.54} \approx 1.7160$, so $A \approx 5000 \times 1.7160 = 8580.00$

Answer:

$P = 5000$, $r = 0.036$, $t = 15$
Equation: $A = 5000e^{0.036t}$
Balance in 15 years: $\$8580.00$