Question

a woman borrowed $3900 from a bank for 6 months. a friend was cosigner of the womans personal note. the bank collected \\(8\frac{1}{2}\\%\\) simple interest on the date of maturity.

a) how much did the woman pay for the use of the money?
b) determine the amount she repaid to the bank on the due date of the note.

a) the woman paid $ for the use of the money.
b) on the due date of the note, the woman repaid $ to the bank.

Explanation:

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<reasoning>

Identify the given values

We begin by extracting the key financial parameters from the problem statement:

• Principal amount borrowed (\(P\)): \(\$3900\)
• Time duration (\(t\)): \(6\text{ months} = \frac{6}{12}\text{ years} = 0.5\text{ years}\)
• Annual simple interest rate (\(r\)): \(8\frac{1}{2}\% = 8.5\% = 0.085\)

Calculate the interest paid

To find how much the woman paid for the use of the money, we calculate the simple interest (\(I\)) generated over the 6-month period.
Using the Simple Interest Formula:
\[
I = P \cdot r \cdot t
\]
Substituting our values:
\[
I = 3900 \cdot 0.085 \cdot 0.5
\]
\[
I = 165.75
\]

Determine the total amount repaid

To find the total amount repaid on the due date (the maturity value, \(A\)), we add the interest accrued to the original principal borrowed.
Using the Maturity Value relation:
\[
A = P + I
\]
Substituting our values:
\[
A = 3900 + 165.75
\]
\[
A = 4065.75
\]
</reasoning>

<answer>

Question a

The woman paid $ <blank>165.75</blank> for the use of the money.

Question b

On the due date of the note, the woman repaid $ <blank>4065.75</blank> to the bank.
</answer>

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]
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Answer:

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</pre_analysis>

<reasoning>

Identify the given values

We begin by extracting the key financial parameters from the problem statement:

• Principal amount borrowed (\(P\)): \(\$3900\)
• Time duration (\(t\)): \(6\text{ months} = \frac{6}{12}\text{ years} = 0.5\text{ years}\)
• Annual simple interest rate (\(r\)): \(8\frac{1}{2}\% = 8.5\% = 0.085\)

Calculate the interest paid

To find how much the woman paid for the use of the money, we calculate the simple interest (\(I\)) generated over the 6-month period.
Using the Simple Interest Formula:
\[
I = P \cdot r \cdot t
\]
Substituting our values:
\[
I = 3900 \cdot 0.085 \cdot 0.5
\]
\[
I = 165.75
\]

Determine the total amount repaid

To find the total amount repaid on the due date (the maturity value, \(A\)), we add the interest accrued to the original principal borrowed.
Using the Maturity Value relation:
\[
A = P + I
\]
Substituting our values:
\[
A = 3900 + 165.75
\]
\[
A = 4065.75
\]
</reasoning>

<answer>

Question a

The woman paid $ <blank>165.75</blank> for the use of the money.

Question b

On the due date of the note, the woman repaid $ <blank>4065.75</blank> to the bank.
</answer>

<post_analysis>
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