Compute the specified quantity.
Your total payment on a 7 year loan, which charged 8.5% annual simple interest, amounted to $60,360. How much did you originally borrow (in dollars)? (Round your answer to the nearest cent.)

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

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

Where:
- $ A $ is the total amount paid (including the original principal and interest).
- $ P $ is the principal (the original loan amount, which we are trying to find).
- $ r $ is the annual interest rate (8.5%, or 0.085 in decimal form).
- $ t $ is the time in years (7 years).

Given:
\[
A = 60,360, \quad r = 0.085, \quad t = 7
\]

Substitute these values into the formula:

\[
60,360 = P(1 + 0.085 \times 7)
\]

First, calculate the term inside the parentheses:

\[
1 + 0.085 \times 7 = 1 + 0.595 = 1.595
\]

Now the equation becomes:

\[
60,360 = P \times 1.595
\]

To find $ P $, divide both sides by 1.595:

\[
P = \frac{60,360}{1.595} \approx 37,835.11
\]

Therefore, the original loan amount was approximately **$37,835.11**.

Would you like further clarification or more details on the calculation?

Here are 5 relative questions:
1. What is the formula for compound interest, and how does it differ from simple interest?
2. How would the loan amount change if the interest rate was compounded annually instead of being simple interest?
3. How would the original loan amount change if the loan term was longer, say 10 years?
4. What would be the total interest paid on this loan?
5. If the annual interest rate were reduced to 6%, what would the original loan amount be?

**Tip:** Always double-check whether the interest is simple or compound when calculating loan payments, as they yield different results.

Your total payment on a 7 year loan, which charged 8.5% annual simple interest, amounted to $60,360. How much did you originally borrow (in dollars)? (Round your answer to the nearest cent.)

Learn how to calculate the original loan amount for a 7-year loan with an 8.5% annual simple interest rate. This detailed solution explains key concepts such as the simple interest formula (A = P(1 + rt)) and provides a step-by-step breakdown. Suitable for students in Grades 9-12.

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