Questions: Jen loaned Barry 14,380 at an interest rate of 8% for 2 years. How much will Barry pay Jen at the end of 2 years? Round your answer to the nearest cent, if necessary.

Jen loaned Barry 14,380 at an interest rate of 8% for 2 years. How much will Barry pay Jen at the end of 2 years? Round your answer to the nearest cent, if necessary.

Transcript text: Jen loaned Barry $\$ 14,380$ at an interest rate of $8 \%$ for 2 years. How much will Barry pay Jen at the end of 2 years? Round your answer to the nearest cent, if necessary.

Solution

Solution Steps

To find out how much Barry will pay Jen at the end of 2 years, we need to calculate the total amount using the formula for simple interest. The formula for simple interest is $ A = P(1 + rt) $, where $ A $ is the total amount, $ P $ is the principal amount, $ r $ is the rate of interest per year, and $ t $ is the time in years. We will substitute the given values into this formula to find the total amount.

Step 1: Identify the Given Values

We are given the following values:

Principal amount ($ P $): $ 14380 $
Interest rate ($ r $): $ 0.08 $
Time ($ t $): $ 2 $

Step 2: Apply the Simple Interest Formula

We will use the simple interest formula to calculate the total amount Barry will pay Jen at the end of 2 years: \[ A = P(1 + rt) \] Substituting the given values into the formula: \[ A = 14380 \left(1 + 0.08 \times 2\right) \]

Step 3: Calculate the Total Amount

Calculating the expression inside the parentheses: \[ 1 + 0.08 \times 2 = 1 + 0.16 = 1.16 \] Now, substituting back into the equation: \[ A = 14380 \times 1.16 = 16680.8 \]