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).