Question

clayton opened a savings account and deposited $300.00 as principal. the account earns 15% interest, compounded continuously. how much interest will he earn after 1 year? round your answer to the nearest cent.

Explanation:

Step1: Recall the formula for continuous compounding

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount of money accumulated after $t$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), and $t$ is the time the money is invested for in years.
First, we need to find the amount $A$ after 1 year, then subtract the principal $P$ to find the interest earned.
Given $P = 300$, $r=0.15$ (since 15% = 0.15), and $t = 1$.

Step2: Calculate the amount $A$

Substitute the values into the formula: $A=300\times e^{0.15\times1}$.
We know that $e^{0.15}\approx1.161834$. So $A = 300\times1.161834=348.5502$.

Step3: Calculate the interest earned

The interest earned $I$ is $A - P$. So $I=348.5502 - 300 = 48.5502$. Rounding to the nearest cent, we get $48.55$.

Answer:

$48.55$