raul deposited $3000 into a bank account that earned simple interest each year. after 3.5 years, he had…

raul deposited $3000 into a bank account that earned simple interest each year. after 3.5 years, he had earned $262.50 in interest. no money was deposited into or withdrawn from the account. what was the annual interest rate? enter your answer in the box.

raul deposited $3000 into a bank account that earned simple interest each year. after 3.5 years, he had earned $262.50 in interest. no money was deposited into or withdrawn from the account. what was the annual interest rate? enter your answer in the box.

Answer

Explanation:

Step1: Recall simple - interest formula

The simple - interest formula is $I = Prt$, where $I$ is the interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We know that $I = 262.50$, $P=3000$, and $t = 3.5$. We need to solve for $r$.

Step2: Rearrange the formula to solve for $r$

Starting with $I = Prt$, we can isolate $r$ by dividing both sides of the equation by $Pt$. So, $r=\frac{I}{Pt}$.

Step3: Substitute the given values into the formula for $r$

Substitute $I = 262.50$, $P = 3000$, and $t=3.5$ into the formula $r=\frac{I}{Pt}$. $r=\frac{262.50}{3000\times3.5}$ First, calculate the denominator: $3000\times3.5 = 10500$. Then, calculate $r$: $r=\frac{262.50}{10500}=0.025$.

Step4: Convert the decimal to a percentage

To convert the decimal $r = 0.025$ to a percentage, multiply by 100. $r=0.025\times100 = 2.5%$

Answer:

$2.5%$