madeline invests money in an account paying simple interest. no money is added or removed from the…

madeline invests money in an account paying simple interest. no money is added or removed from the investment. to find the balance after a year, she multiplies her current balance by 1.051. what percent simple interest does the account earn per year?

madeline invests money in an account paying simple interest. no money is added or removed from the investment. to find the balance after a year, she multiplies her current balance by 1.051. what percent simple interest does the account earn per year?

Answer

Explanation:

Step1: Recall simple - interest formula

The formula for simple interest is $A = P(1 + rt)$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the interest rate, and $t$ is the time in years. In this case, $t = 1$ year, so $A=P(1 + r)$. We know that $A = 1.051P$.

Step2: Solve for the interest rate $r$

Since $A = P(1 + r)$ and $A = 1.051P$, we can set up the equation $P(1 + r)=1.051P$. Divide both sides of the equation by $P$ (since $P\neq0$), we get $1 + r=1.051$. Then subtract 1 from both sides: $r=1.051 - 1=0.051$.

Step3: Convert $r$ to a percentage

To convert a decimal to a percentage, we multiply by 100. So $r = 0.051\times100% = 5.1%$.

Answer:

$5.1%$