A $10,000 loan is to be repaid at the rate of $200 per month, with an annual effective interest rate of 19.56% charged against the unpaid balance. What principal remains to be paid after the third payment? (a) 9500 (b) 9800 (c) 8900 (d) 9200

To solve this problem, we need to understand how the loan repayment works. The loan is repaid at a rate of $200 per month, with an annual effective interest rate of 19.56% charged against the unpaid balance.

Step 1: Convert the annual interest rate to a monthly rate. The annual effective interest rate is 19.56%, so the monthly interest rate is (1 + 19.56/100)^(1/12) - 1 = 0.0149 or 1.49%.

Step 2: Calculate the remaining balance after each payment. After the first payment, the remaining balance is $10,000 -$200 = $9800. Then, the interest for the first month is$9800 * 1.49% = $146.02. So, the balance at the end of the first month is$9800 + $146.02 =$9946.02.

After the second payment, the remaining balance is $9946.02 -$200 = $9746.02. Then, the interest for the second month is$9746.02 * 1.49% = $145.16. So, the balance at the end of the second month is$9746.02 + $145.16 =$9891.18.

After the third payment, the remaining balance is $9891.18 -$200 = $9691.18. Then, the interest for the third month is$9691.18 * 1.49% = $144.40. So, the balance at the end of the third month is$9691.18 + $144.40 =$9835.58.

So, the principal that remains to be paid after the third payment is approximately $9836, which is not exactly any of the options given. However, it is closest to (b) 9800.