An $8,000 demand loan at a fixed simple interest rate of 10.5% was advanced on May 10. A payment of $2,000 was made on July 15 and a final payment was made on Sept. 5. What was the size of the final payment?

A) $6,241.64
B) $6,243.92
C) $6,363.61
D) $6,151.89
E) $8,152.90

To calculate the final payment, we first need to determine the interest accrued on the loan. The loan starts on May 10, and the first payment is made on July 15, which is 66 days later (31 days in May, minus 10 days, plus 30 days in June, plus 15 days in July).The interest for this period on the initial $8,000 at a 10.5% annual rate is calculated as follows:Interest = Principal × Rate × Time = $8,000 × 10.5% × (66/365) = $8,000 × 0.105 × 0.1808 = $151.89.After the first payment of $2,000 on July 15, the principal is reduced to $6,000. The next and final payment is made on Sept 5, which is 52 days after July 15 (16 days in July, plus 31 days in August, plus 5 days in September).The interest for this period on the remaining $6,000 at a 10.5% annual rate is calculated as follows:Interest = Principal × Rate × Time = $6,000 × 10.5% × (52/365) = $6,000 × 0.105 × 0.1425 = $90.03.Therefore, the total interest accrued over the entire period is $151.89 + $90.03 = $241.92.The final payment must cover the remaining principal of $6,000 plus the accrued interest of $241.92, totaling $6,241.92.