On may 19, Betty borrowed $3,000 from the bank at a rate of 12%. The loan is to be repaid on October 8. Assuming the loan is based on exact interest, what’s the total interest cost to betty

To find the total interest cost for Betty, we need to use the formula for exact simple interest:

\[
I = P \times r \times t
\]

Where:
- $I$ = Interest
- $P$ = Principal amount ($3,000)
- $r$ = Annual interest rate (12% or 0.12)
- $t$ = Time in years

### Step 1: Determine the Time (t)
We need to calculate the time between May 19 and October 8. Since the problem specifies that the loan is based on exact interest, we will count the actual days between these two dates.

- May 19 to May 31: $31 - 19 = 12$ days
- June has 30 days
- July has 31 days
- August has 31 days
- September has 30 days
- October 1 to October 8: 8 days

So, the total number of days is:

\[
12 + 30 + 31 + 31 + 30 + 8 = 142 \text{ days}
\]

Since there are 365 days in a year, the time in years is:

\[
t = \frac{142}{365} \approx 0.389
\]

### Step 2: Calculate the Interest
Now, we can plug in the values into the interest formula:

\[
I = 3000 \times 0.12 \times 0.389
\]

\[
I \approx 140.04
\]

So, the total interest cost to Betty is **$140.04**.

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Would you like further details on this solution or have any other questions?

Here are 5 related questions:
1. What would the interest be if the loan rate was 10% instead of 12%?
2. How would the interest change if the loan was for a full year?
3. What is the difference between exact interest and ordinary interest?
4. How does compound interest differ from simple interest in this case?
5. What would happen if the loan was repaid earlier, say in September?

**Tip**: When calculating time for interest, ensure you know if the problem refers to exact days or assumes a 360-day year (ordinary interest).

On May 19, Betty borrowed $3,000 from the bank at a rate of 12%. The loan is to be repaid on October 8. Assuming the loan is based on exact interest, what’s the total interest cost to Betty?

Learn how to calculate the exact interest on a $3,000 loan borrowed at a rate of 12% for 142 days. Using the simple interest formula, this example breaks down each step from calculating the time period to determining the final interest cost, suitable for Grades 9-10.

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