Question

wyatt had $3,200 in a savings account with simple interest. he had opened the account with $2,000 exactly 4 years earlier. 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.

Explanation:

Step1: Find the interest earned (i)

The principal (p) is $2000, and the final amount is $3200. So the interest earned \( i = 3200 - 2000 = 1200 \).

Step2: Identify p, t values

We know \( p = 2000 \), \( t = 4 \) years, and \( i = 1200 \). Use the formula \( i = prt \) to solve for \( r \).
Substitute the values into the formula: \( 1200 = 2000 \times r \times 4 \).

Step3: Solve for r

First, simplify the right - hand side: \( 2000\times4\times r=8000r \).
So we have the equation \( 1200 = 8000r \).
To solve for \( r \), divide both sides by 8000: \( r=\frac{1200}{8000}=0.15 \).
To convert this decimal to a percentage, multiply by 100: \( 0.15\times100 = 15\% \).

Answer:

15