Daryl borrowed $5,707 for 8 years. If the loan's annual simple discount rate was 3.4%, how much did he have to return?

Round your answer to the nearest dollar. 

To determine how much Daryl has to return for the loan, we'll use the formula for the maturity value (or the amount to be repaid) under a simple discount loan. This formula is:

\[
M = \frac{P}{1 - dt}
\]

Where:
- $ M $ is the maturity value (the amount Daryl has to return),
- $ P $ is the principal or the amount borrowed, which is $5,707,
- $ d $ is the discount rate, which is 3.4% (or 0.034),
- $ t $ is the time of the loan, which is 8 years.

Let's plug in the values and calculate.

\[
M = \frac{5707}{1 - (0.034 \times 8)}
\]

Now I’ll calculate the result.Daryl will have to return **$7,839** after 8 years.

Do you want more details or have any questions about this?

Here are 5 related questions for further exploration:
1. How is the maturity value different in simple interest versus simple discount loans?
2. What would happen if the discount rate increased to 4%?
3. How can we calculate the amount Daryl borrowed if we only know the repayment amount and the discount rate?
4. What is the difference between simple and compound interest in loan calculations?
5. How would Daryl’s repayment change if the loan period were extended by 2 years?

**Tip:** Always verify whether the interest type is simple or compound, as it significantly affects the total amount to be repaid.

Daryl borrowed $5,707 for 8 years. If the loan's annual simple discount rate was 3.4%, how much did he have to return? Round your answer to the nearest dollar.

Discover how to calculate the maturity value of a simple discount loan where $5,707 was borrowed for 8 years at a 3.4% annual discount rate. This problem covers key concepts like the simple discount formula and basic algebra, suitable for students in Grades 9-12.

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