$46.$ Calculating Annuities Due Suppose you are going to receive $$14,500$ per year for five years. The appropriate discount rate is$7\mathrm{.}1$ percent.a$.$ What is the present value of the payments if they are in the form of an ordinary annuity? What is the present value if the payments are an annuity due?b$.$ Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity?What if the payments are an annuity due?c$.$ Which has the higher present value, the ordinary annuity or annuity due? Which has the higher future value? Will this always be true?$10147.$Annuity and Perpetuity Values Mary is going to receive a $30-$year annuity of $$11,500$ per year. Nancy is going to receive a i perpetuity of $$11,500$ per year. If the appropriate discount rate is $4\mathrm{.}3$ percent, how much more is Nancy's cash flow worth?L$0148.$Calculating Present Values A six$-$year annuity of twelve $$8\mathrm{.}250$ semiannual payments will begin nine years from now, with the first payment coming $9\mathrm{.}5$ years from now. If the discount rate is $8$ percent compounded semiannually, what is the value of this annuity five years from now? What is the value three years from now? What is the current value of the annuity?LO$149.$Present Value and Multiple Cash Flows What is the value today of $$5\mathrm{.}100$ per year, at a discount rate of $7\mathrm{.}9$ percent, if the first payment is received six years from today and the last payment is received $20$ years from today?LO$150.$Variable Interest Rates A $15-$year annuity pays $81\mathrm{.}750$ per month, and payments are made at the end of each month. If the interest rate is $9$ percent compounded monthly for the first seven years, and $6$ percent compounded monthly thereafter, what is the value of the annuity today?LO$151.$Comparing Cash Flow Streams You have your choice of two investment accounts. Investment A is a $13-$year annuity that features end$-$of$-$month $$1,600$ payments and has an APR of $7\mathrm{.}8$ percent compounded monthly. Investment B is an annually compounded lump$-$sum investment with an interest rate of $9$ percent, also good for $13$ years. How much money would you need to invest in B today for it to be worth as much as Investment A $13$ years from now?Page $164$LO$152.$Calculating Present Value of a Perpetuity Given a discount rate of $4\mathrm{.}6$ percent per year, what is the value at Date t $=7$ of aperpetual stream of $$7,300$ payments with the first payment at Date t $=15?$