- Identify the principal \(P = 10,000\), the interest rate \(r = 0.05\), and the time \(t = 4\).
- Use the simple interest formula \(I = P \times r \times t\).
- Multiply the values: \(10,000 \times 0.05 \times 4 = 2,000\).
- The total interest paid by the end of the loan term is \(\boxed{\$2,000}\).
Explanation
- Problem Analysis and Formulas
The objective is to calculate the total interest paid on a loan of \(\$10,000\) with an annual interest rate of \(5\%\) over a period of \(4\) years, using the simple interest model. The principal amount is \(P = \$10,000\), the annual interest rate is \(r = 5\% = 0.05\), and the duration of the loan is \(t = 4\) years. The simple interest formula for the total amount \(A\) is \(A = P(1 + rt)\), and the interest \(I\) itself is given by the formula \(I = P \times r \times t\).
- Calculating the Interest Amount
To find the interest \(I\), we substitute the given values into the formula \(I = P \times r \times t\):
\[I = 10,000 \times 0.05 \times 4\]
First, calculate the product of the principal and the rate:
\[10,000 \times 0.05 = 500\]
Next, multiply this result by the time period:
\[500 \times 4 = 2,000\]
Thus, the total interest Griffin will pay is \(\$2,000\). Comparing this result to the given options:
A\(\$2,000\)
B\(\$500\)
C\(\$2,500\)
D\(\$5,000\)
The correct option is (a).
Examples
Simple interest calculations are essential in personal finance. For example, when you take out a car loan or a personal loan, the bank often charges interest based on the initial principal. By understanding how to calculate this, you can better manage your budget, compare different loan offers, and understand the total cost of borrowing money over time. Ensuring you calculate interest correctly helps you make informed financial decisions.