On May 19, Bette Santoro borrowed $3,000 from Resse Bank at a rate of 12½%. The loan is to be repaid on October 8. Assuming the loan is based on exact interest, what's the total interest cost to Bette?
A. $265.89
B. $175.89
C. $145.89
D. $345.89
The closest answer I got was $375 but I know that isn't right.
I did 3000* 12 1/2%.
I could really use someone's help with this.
Bette didn't borrow the money for a year. She borrowed it for 142 days.
142/365 * 375 = _________
To calculate the total interest cost for Bette, we need to determine the interest accrued over the period from May 19 to October 8.
Step 1: Calculate the number of days between the two dates.
May 19 to October 8 is a total of 142 days.
Step 2: Convert the interest rate to a decimal.
12½% is equal to 0.125 in decimal form.
Step 3: Calculate the interest accrued.
The formula to calculate simple interest is:
Interest = Principal × Rate × Time
Interest = $3,000 × 0.125 × (142/365)
Step 4: Calculate the total interest cost.
Total Interest Cost = Principal + Interest accrued
Total Interest Cost = $3,000 + (Interest)
Now, let's plug in the numbers to calculate the total interest cost for Bette.
Interest = $3,000 × 0.125 × (142/365)
Interest ≈ $105.41
Total Interest Cost = $3,000 + $105.41
Total Interest Cost ≈ $3,105.41
None of the given answer choices match the calculated total interest cost of $3,105.41. Hence, it appears that there might be an error in the options provided.
To calculate the interest cost for Bette's loan, we need to know the number of days between May 19 and October 8. Let's break down the steps to find the correct answer.
Step 1: Calculate the number of days between May 19 and October 8.
To do this, we need to count the number of days in each month. From May 19 to the end of May, there are 12 days. In June, there are 30 days. In July, there are 31 days. In August, there are 31 days. In September, there are 30 days. And finally, up to October 8, there are 8 days.
So the total number of days between May 19 and October 8 is 12 + 30 + 31 + 31 + 30 + 8 = 142 days.
Step 2: Calculate the interest cost using the exact interest formula.
The exact interest formula is: Interest = (Principal * Rate * Time) / 100
Given:
Principal (amount borrowed) = $3,000
Rate = 12 ½% = 12.5% = 0.125 (decimal form)
Time = number of days / 365
Using these values, we can calculate the interest cost:
Interest = (3000 * 0.125 * 142) / 365
Step 3: Calculate the interest cost.
Using a calculator, we can find the interest cost to be approximately $147.671 or rounded to the nearest cent, $147.67.
None of the provided answer options match this amount exactly, so it seems there might be a slight rounding error or discrepancy in the available choices. However, the closest answer is C. $145.89.
Please keep in mind that this calculation assumes the loan is based on exact interest, which means there are no additional fees or compounding involved. The actual repayment terms of the loan may vary, so it's always best to consult with the lender or refer to the loan agreement for precise details.