Question

financial literacy fabiana opened a savings account with $14,200 that earns 12% simple interest annually. after how many years will the balance of the account be $15,478.2? round to the nearest tenth, if necessary. years incorrect 2 tries left. please try again.

Explanation:

Step1: Recall simple - interest formula

The simple - interest formula is $A = P(1+rt)$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Given $P=\$14200$, $r = 0.12$, and $A=\$15478.2$. We need to solve for $t$.
First, substitute the values into the formula: $15478.2=14200(1 + 0.12t)$.

Step2: Divide both sides by 14200

$\frac{15478.2}{14200}=1 + 0.12t$.
$1.09 = 1+0.12t$.

Step3: Subtract 1 from both sides

$1.09−1 = 0.12t$.
$0.09 = 0.12t$.

Step4: Solve for t

$t=\frac{0.09}{0.12}$.
$t = 0.75$ years.

Answer:

$0.75$ years