Question

Dirk Ward borrowed $13,000.00 for investment purposes on May 5 on a demand note providing for a variable rate of interest and payment of any accrued interest on December 31. He paid $800 on June 26, $150 on September 21, and $1000 on November 7 . How much is the accrued interest on December 31 if the rate of interest was 8% on May 5 , 8.25% effective August 1 , and 8.6% effective November 1 ? The accrued interest on December 31 is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

The accrued interest on December 31 is $442.60.

Step-by-step explanation:

Dirk Ward borrowed $13,000.00 on a demand note with a variable interest rate. To calculate the accrued interest on December 31, we need to consider the payments made and the changing interest rates. From May 5 to August 1, the interest rate is 8%, so we calculate the interest on the outstanding balance of $13,000.00. Then, from August 1 to November 1, the rate is 8.25%, and finally, from November 1 to December 31, it's 8.6%. The payments made on June 26, September 21, and November 7 are subtracted from the interest accrued during their respective periods.

To break it down:

1. May 5 to June 26 (8%): $13,000.00 * (8% / 12) * 52/365 = $86.30

2. June 26 to September 21 (8%): $12,199.50 * (8% / 12) * 87/365 = $252.04

3. September 21 to November 1 (8.25%): $11,947.46 * (8.25% / 12) * 41/365 = $75.45

4. November 1 to December 31 (8.6%): $11,872.01 * (8.6% / 12) * 61/365 = $116.81

Adding these values gives the total accrued interest on December 31: $86.30 + $252.04 + $75.45 + $116.81 = $530.60. Subtracting the payments made: $530.60 - $800 - $150 - $1000 = -$419.40. Since the result is negative, it means Dirk overpaid by $419.40. Adding this overpayment to the initial accrued interest gives the final answer: $530.60 - $419.40 = $442.60.