(Present value of a perpetuity) At a discount rate of 15.50%, find the present value of a perpetual payment of $8,000 per year. If the discount rate were lowered to 7.75%, half the initial rate, what would be the value of the perpetuity? a. If the discount rate were 15.50%, the present value of the perpetuity is $ (Round to the nearest cent.) b. If the discount rate were lowered to 7.75%, half the initial rate, the present value of the perpetuity is $ cent.) (Round to the nearest (Components of annuity payments) You've just taken on a 20-year, $150,000 mortgage with a quoted interest rate of 6 percent calling for payments semiannually. How much of your first year's loan payments (the initial two payments, with the first coming after 6 months have passed, and the second one coming at the end of the first year) goes toward paying interest, rather than principal? a. What is the semiannual payment of your loan? (Round to the nearest cent.) b. How much of your first year's 2 loan payments goes toward paying interest, rather than principal? (Round to the nearest cent.) $ (Present value of complex cash flows) How much do you have to deposit today so that beginning 11 years from now you can withdraw $10,000 a year for the next 5 years (periods 11 through 15) plus an additional amount of $20,000 in the last year (period 15)? Assume an interest rate of 6 percent. The amount of money you have to deposit today is $ (Round to the nearest cent.)