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We are asked to determine the simple interest rate for a student loan.

### Given:
- Loan amount $ P = 5000 $ dollars
- Time period $ t = 3 $ years
- Monthly payment $ PMT = 152.35 $ dollars
- Total payments made $ 152.35 \times 12 \times 3 $

### Total Amount Paid:
\[
\text{Total Amount Paid} = 152.35 \times 12 \times 3 = 5484.60 \text{ dollars}
\]

### Interest Paid:
The interest paid is the total amount paid minus the principal:
\[
I = 5484.60 - 5000 = 484.60 \text{ dollars}
\]

### Formula for Simple Interest:
The simple interest formula is:
\[
I = P \times r \times t
\]
where:
- $ I $ is the interest paid
- $ P $ is the principal (loan amount)
- $ r $ is the annual interest rate
- $ t $ is the time in years

Now, solve for $ r $:
\[
r = \frac{I}{P \times t} = \frac{484.60}{5000 \times 3} = \frac{484.60}{15000} = 0.03231
\]

### Final Result:
The simple interest rate is approximately $ 3.23\% $.

Would you like further details on any steps?

### Related questions:
1. What is the difference between simple and compound interest?
2. How would the monthly payment change if the loan term was 5 years instead of 3?
3. How do you calculate the interest if the rate is compounded annually?
4. How would the interest change if the loan was $10,000 instead of $5,000?
5. How does the interest rate affect the total amount paid on a loan?

#### Tip:
When calculating interest, always ensure the time units for rate and loan term are consistent (e.g., both in years).

Mateo’s sister paid off her student loan of $5000 in 3 years. If she made a payment of $152.35 each month, what was the simple interest rate for her loan? Round to the nearest hundredth.

Learn how to calculate the simple interest rate for a $5000 student loan, paid off in 3 years with monthly payments of $152.35. Follow a detailed step-by-step guide using simple interest formulas and key algebraic concepts. Suitable for students in Grades 10-12.

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