I need help with problems 10-13 and how to do them step by step.

Determine the discount points necessary to provide a yield-to-matur 10 percent for the following mortgages with 30-year maturities. f 5-10. AMOUNT AT DISCOUNT MONTHLY MORTGAGE PAYMENT (S) COUPON RATE ORIGINATION (S) POINTS (IN $800 900 950 700 N/A N/A N/A N/A 100,000 110,000 125,000 110,000 Determine the balance of the following 30-year mortgages at the end of the fifth year. (Hint: The balance of a standard fixed-rate mortgage at any time is equal to the present value of the remaining payments dis- counted by the rate on the mortgage.) 5-11. MORTGAGE ORIGINAL AMOUNT (S) CONTRACT RATE () BALANCE 100,000 90,000 80,000 12 Suppose that a lender offers you a 15-year, monthly payment mortgage for $120,000 at 6 percent with two discount points. a. Calculate your monthly payment. b. What is the APR on this loan? c. What is the effective cost if the loan is repaid at the end of year 8? To buy your dream home you use a 10/20 interest-only, fixed-rate mort- gage. The loan has monthly payments and is for $110,000 at 7.50 per- cent. The lender charges you two discount points. a. What is your payment for the initial interest-only period? b. What is your payment over the 20-year amortization period? c. What is the APR on the loan? d. What is the effective cost of the loan if it is repaid 6 years after the 5-12. 5-13. interest-only period