Compute the specified quantity.
Your total payment on a 3 year loan, which charged 7.5% annual simple interest, amounted to $70,360. How much did you originally borrow (in dollars)? (Round your answer to the nearest cent.)
$ 

To find out how much you originally borrowed, we can use the formula for simple interest:

\[
A = P(1 + rt)
\]

Where:
- $A$ is the total amount paid (principal + interest),
- $P$ is the principal (original loan amount),
- $r$ is the annual interest rate (as a decimal),
- $t$ is the time in years.

Given:
- Total payment $A = 70,360$,
- Interest rate $r = 7.5\% = 0.075$,
- Time $t = 3$ years.

We need to solve for $P$, the original loan amount. Rearrange the formula to solve for $P$:

\[
P = \frac{A}{1 + rt}
\]

Substitute the known values into the equation:

\[
P = \frac{70,360}{1 + (0.075 \times 3)}
\]

Simplify the equation:

\[
P = \frac{70,360}{1 + 0.225} = \frac{70,360}{1.225}
\]

Now, divide:

\[
P = 57,439.18
\]

So, the original amount borrowed was approximately **$57,439.18**.

Would you like more details or have any questions? Here are some related questions to consider:

1. What would be the total payment if the interest rate was compounded annually?
2. How would the total payment change if the loan was for 5 years instead of 3?
3. How do you calculate monthly payments for a loan with simple interest?
4. What is the difference between simple interest and compound interest in terms of overall cost?
5. How can you reduce the total interest paid on a loan?

**Tip:** Always double-check loan terms for simple vs. compound interest, as the total cost can vary significantly.

Your total payment on a 3 year loan, which charged 7.5% annual simple interest, amounted to $70,360. How much did you originally borrow (in dollars)? (Round your answer to the nearest cent.)

Learn how to calculate the original loan amount using simple interest. The total payment for a 3-year loan with 7.5% interest is $70,360. Use the simple interest formula A = P(1 + rt) to find the amount borrowed, suitable for students in Grades 9-12.

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