roger opened a savings account and deposited $100.00 as principal. the account earns 3% interest, compounded…

roger opened a savings account and deposited $100.00 as principal. the account earns 3% interest, compounded continuously. what is the balance after 1 year? use the formula $a = pe^{rt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $e$ is the base of natural logarithms ($\\approx2.71828$), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years. round your answer to the nearest cent.

roger opened a savings account and deposited $100.00 as principal. the account earns 3% interest, compounded continuously. what is the balance after 1 year? use the formula $a = pe^{rt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $e$ is the base of natural logarithms ($\\approx2.71828$), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years. round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify the values of P, r, and t

$P = 100$, $r=0.03$, $t = 1$

Step2: Substitute values into the formula

$A=Pe^{rt}=100\times e^{0.03\times1}$

Step3: Calculate the value of $A$

$A = 100\times e^{0.03}\approx100\times1.0304545 = 103.05$ (rounded to the nearest cent)

Answer:

$103.05$