kira deposited $1,200 in a savings account with simple interest. four months later, she had earned $43.60 in…

kira deposited $1,200 in a savings account with simple interest. four months later, she had earned $43.60 in interest. what was the interest rate? use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

kira deposited $1,200 in a savings account with simple interest. four months later, she had earned $43.60 in interest. what was the interest rate? use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Answer

Explanation:

Step1: Convert time to years

Since there are 12 months in a year, $t=\frac{4}{12}=\frac{1}{3}$ years.

Step2: Rearrange the simple - interest formula for $r$

Given $i = prt$, we can solve for $r$ by dividing both sides of the equation by $pt$. So $r=\frac{i}{pt}$.

Step3: Substitute the given values

We know that $i = 43.60$, $p = 1200$, and $t=\frac{1}{3}$. Then $r=\frac{43.60}{1200\times\frac{1}{3}}$. First, calculate $1200\times\frac{1}{3}=400$. Then $r=\frac{43.60}{400}=0.109$.

Step4: Convert $r$ to a percentage

To convert a decimal to a percentage, multiply by 100. So the interest rate as a percentage is $r = 0.109\times100 = 10.9%$.

Answer:

$10.9$