Jake received a student loan for $12,000. He plans on paying off the loan in 5 years. At the end of 5 years, Jake will have paid $3,600 in interest. What is the simple interest rat... Jake received a student loan for $12,000. He plans on paying off the loan in 5 years. At the end of 5 years, Jake will have paid $3,600 in interest. What is the simple interest rate on the student loan?
Understand the Problem
The question is asking for the calculation of the simple interest rate based on the loan amount, the amount of interest paid, and the time period of the loan. To solve it, we need to use the simple interest formula and rearrange it to find the interest rate.
Answer
The simple interest rate on the student loan is \( 6\% \).
Answer for screen readers
The simple interest rate on the student loan is ( 6% ).
Steps to Solve
- Identify Given Information
The problem states that Jake has a loan amount of $12,000, he will pay $3,600 in interest, and the loan period is 5 years.
- Use the Simple Interest Formula
The formula for simple interest is:
$$ I = P \times r \times t $$
where:
- ( I ) is the interest paid,
- ( P ) is the principal (loan amount),
- ( r ) is the interest rate (as a decimal),
- ( t ) is the time (in years).
- Substitute Known Values
We know:
- ( I = 3600 )
- ( P = 12000 )
- ( t = 5 )
Substituting these values into the formula:
$$ 3600 = 12000 \times r \times 5 $$
- Rearrange the Equation to Solve for ( r )
First, simplify the equation:
$$ 3600 = 60000 \times r $$
Now, solve for ( r ):
$$ r = \frac{3600}{60000} $$
- Calculate the Interest Rate
Perform the division:
$$ r = 0.06 $$
- Convert to Percentage
To convert the decimal to a percentage, multiply by 100:
$$ r = 0.06 \times 100 = 6% $$
The simple interest rate on the student loan is ( 6% ).
More Information
Jake's loan has a straightforward interest rate of 6%, which is quite typical for student loans. Understanding simple interest is crucial for managing loans effectively.
Tips
- Forgetting to convert the decimal interest rate to a percentage.
- Mixing up the values when substituting into the formula. Be careful to maintain the correct values for principal, interest, and time.
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