For part A, your calculation is correct. That is what the amount of the loan would be if no payments were made. Of course, the bank would not allow that.

For part B, you got the correct answer for the payment to pay off the loan over 30 years. The payments are smaller because they are paid earlier.

I think they're asking for something different in part B. They say the amount paid off after one month is D dollars - I think they want you to calculate what the payments would be worth if they were in a separate account. Otherwise they should have said D-750, where $750 is the principal times the monthly interest rate ($100,000 * 0.0075). So after two months, it would be 1.0075D + D. The first month's payment grew by 0.75%, and then the second month's payment was added in. After n months, you would have D times 1 + 1.0075 + ... + (1.0075)^(n-1).

This is a finite geometric series - have you learned how to calculate the sum?

- Hollywood