Math Problem Statement

Eric's car loan statement said he would pay $6,718.02 in interest for a 5 year loan at 8.3% . How much did Eric borrow to buy the car?

Solution

We can calculate how much Eric borrowed to buy the car by using the formula for simple interest:

I=P×r×tI = P \times r \times t

Where:

  • II is the interest paid ($6,718.02),
  • PP is the principal (the amount borrowed),
  • rr is the annual interest rate (8.3% or 0.083),
  • tt is the time in years (5 years).

Rearranging the formula to solve for PP:

P=Ir×tP = \frac{I}{r \times t}

Now, substituting the given values:

P=6,718.020.083×5P = \frac{6,718.02}{0.083 \times 5}

Let’s calculate it:

P=6,718.020.415P = \frac{6,718.02}{0.415}

P16,190.64P \approx 16,190.64

So, Eric borrowed approximately $16,190.64 to buy the car.

Would you like more details or have any further questions?

Here are 5 related questions:

  1. What is the formula for compound interest?
  2. How does the interest rate affect the total interest paid over time?
  3. What would the interest be if Eric had a 7-year loan instead of 5 years?
  4. How would the principal change if the interest rate was reduced to 6%?
  5. Can monthly payments be calculated using the same formula for interest?

Tip: Always check whether the interest is simple or compounded when calculating loans or investments.

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Math Problem Analysis

Mathematical Concepts

Simple Interest
Algebra

Formulas

I = P × r × t
P = I / (r × t)

Theorems

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Suitable Grade Level

Grades 9-11