1. (a) Given the nominal annual rate of interest compounded monthly is 12%, nd the effective rate of interest per month. What is its equivalent effective rate of interest per annum? (b) Given the nominal annual rate of interest compounded semiannually is 8%, nd the effective rate of interest per month. (c) Given that the effective rate of interest per year is 6%, nd the nominal annual rate of interest convertible 12 times and 2 times per year, respectively. 2. A loan of amount $10, 000 at a nominal annual interest rate of 9% compounded monthly is repaid by monthly payments over two years, starting one month after the loan is made. (a) Find the monthly payment. (b) Calculate the interest portion and the principal portion within the rst two monthly installments. (c) Find the outstanding loan balance after one year. ((1) Find the total cost of this loan. (e) If the monthly payment is doubled for the second year, nd the monthly payment amount for the second year. 3. John borrows $20,000 to purchase a car. The car dealer nances the purchase and offers John two alternative nancing plans, both of which require monthly payments at the end of each months for 4 years starting one month after the car is purchased: (i) 12% nominal annual interest rate compounded monthly for the 4 years; (ii) a cash back of $1, 000 and 15% nominal annual interest rate compounded monthly for the 4 years. Assuming the $1, 000 cash back is used to reduce the amount of the loan, which offer is more attractive to the purchaser by comparing their respective monthly payment? 4. A home buyer borrow $350, 000 to be repaid over a 25year period with level monthly pay ments beginning one month after the mortgage is taken. The interest rate on this mortgage is a nominal annual rate of 5% compounded semiannually. (a) Find the monthly payment. (b) The mortgage is renegotiated after the rst 5year term. Suppose that the new nominal annual rate compounded semiannually for the second 5-year term is 4%. Find the monthly payment during the second 5year term