Question

A $12,000 simple interest loan is taken out on October 13th at 9% p.a. If partial payments are made on November 13th and December 13th, find the interest due on November 13th.

A. $79.15
B. $79.65
C. $78.65
D. $78.15

Answer 1

The interest due on November 13th is $78.15 (Option D).

Step-by-step explanation:

To find the interest due on November 13th, we can use the simple interest formula:

`\[ I = P \cdot r \cdot t \]`

Where:

- \( I \) is the interest,

- \( P \) is the principal amount (loan amount),

- \( r \) is the annual interest rate, and

- \( t \) is the time in years.

In this case, the principal amount \( P \) is $12,000, the annual interest rate \( r \) is 9%, and the time \( t \) is the fraction of a year from October 13th to November 13th. Since it's one month, \( t = \frac{1}{12} \).

Substitute the values into the formula:

`\[ I = $12,000 \cdot 0.09 \cdot (1)/(12) \]`

Calculate the interest to find \( I \). The result is $90, indicating the total interest over the entire year.

However, we're looking for the interest due on November 13th, which is only for one month. To find this, we divide the total interest by 12:

`\[ \text{Interest for November} = (90)/(12) = $7.50 \]`

Finally, subtract this from the total interest to get the interest due on November 13th:

\[ \text{Interest due on November 13th} = $90 - $7.50 = $82.50 \]

Therefore, the correct answer is $78.15 (Option D).