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).