Problem Set 1. A man is paying off a debt of $15,000 with regular payments of $300 at the end of each month. Annual interest is 18% compounded monthly. (a) Find the exact amount of time to at least five decimal places that it will take to pay off this loan. (b) Determine the size of the balloon payment to be made to pay off the loan at the time of the last regular payment. (c) Determine the size of the drop payment which would have to be made one month after the last regular payment. d) How long would it take to pay off the original debt of $15,000 if the payment at the end of each month were $225? 2. A debt of $50,000 is being repaid with regular monthly payments of $1000 at 15% per annum compounded monthly. How many of the regular $1000 monthly payments will be necessary and what will be the amount of the last payment which will be made one! month after the last regular payment? 3. A fund of $1750 is to be accumulated by means of level deposits of $100 to be made at the end of each year for as long as necessary. If this fund earns an effective rate of interest of 7% per annum (a) How many level deposits of $100 will be necessary and what would be the size of the balloon payment to be made at the time of the last level payment?! (b) What would the size of the drop payment that would have to be made one year after the last level payment? (C) What would be the size of the drop payment that would have to be made three months after the last level payment? 4. Consider an annuity paying $150 every month at 18% compounded monthly. How many payments will be necessary and what would be the balloon payment, drop payment, and fractional payment (as in Example 3.6) to amount to exactly $15,000? 5. We wish to accumulate a fund of $60,000 by making regular deposits of $1,525 at the end of each month for as long as is necessary. If the annual rate of interest is 6% compounded monthly, how many regular deposits will be necessary and find the final deposit to be made one month after the last regular deposit