Jack received a student loan for $12,000. What is the simple interest rate on the loan if he will have paid $3,600 off the loan at the end of 5 years?
Understand the Problem
The question is asking us to calculate the simple interest rate for a student loan taken out for $12,000 with a given interest amount of $3,600 over 5 years. We need to find the rate of interest based on this information.
Answer
The simple interest rate is $6\%$.
Answer for screen readers
The simple interest rate is $r = 6%$.
Steps to Solve
-
Identify the variables
We have the following information:
- Principal amount (P) = $12,000
- Total interest (I) = $3,600
- Time (t) = 5 years
-
Use the simple interest formula
The formula for calculating simple interest is given by: $$ I = P \times r \times t $$ where $r$ is the rate of interest (as a decimal).
-
Rearrange the formula to solve for the rate
To find $r$, rearrange the formula: $$ r = \frac{I}{P \times t} $$
-
Substitute the known values into the formula
Substitute $I = 3600$, $P = 12000$, and $t = 5$: $$ r = \frac{3600}{12000 \times 5} $$
-
Calculate the rate
Perform the calculations:
- First calculate $12000 \times 5 = 60000$.
- Then calculate $r = \frac{3600}{60000} = 0.06$ or 6%.
The simple interest rate is $r = 6%$.
More Information
The interest rate shows how much the borrower pays for using the lender's money. A rate of 6% means that the borrower will pay 6% of the principal amount as interest annually.
Tips
- Forgetting to convert the rate from a decimal to a percentage.
- Incorrectly calculating the total amount ($P \times t$) which can lead to an incorrect rate.
AI-generated content may contain errors. Please verify critical information
