scott opened a savings account and deposited $1,000.00. the account earns 2% interest, compounded…

scott opened a savings account and deposited $1,000.00. the account earns 2% interest, compounded continuously. if he wants to use the money to buy a new bicycle in 1 year, how much will he be able to spend on the bike? 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.

scott opened a savings account and deposited $1,000.00. the account earns 2% interest, compounded continuously. if he wants to use the money to buy a new bicycle in 1 year, how much will he be able to spend on the bike? 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

$P = 1000$, $r=0.02$, $t = 1$

Step2: Substitute values into the formula

$A=Pe^{rt}=1000\times e^{0.02\times1}$

Step3: Calculate the value of A

$A = 1000\times e^{0.02}\approx1000\times1.02020134 = 1020.20134$

Step4: Round to the nearest cent

$A\approx1020.20$

Answer:

$1020.20$