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Assume that Social Security promises you $38,000 per year starting when you retire 45 years from today (the first $38,000 will get paid 45 years from now). If your discount rate is 10%, compounded annually, and you plan to live for 14 years after retiring (so that you will receive a total of 15 payments including the first one), what is the value today of Social Security's promise? A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $5,000. Each year after that, you will recelve a payment on the anniversary of the last payment that is 2% larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is 10% per year. a. What is today's value of the bequest? b. What is the value of the bequest immediately after the first payment is made? You are thinking about buying a savings bond. The bond costs $44 today and will mature in 15 years with a value of $88. What annual interest rate will the bond eam? The bond will earn an annual rate of \%. (Round to two decimal places.) You have decided to buy a perpetual bond. The bond makes one payment at the end of every year forever and has an interest rate of 8%. If the bond initially costs $3,000, what is the payment every year? The payment at the end of each year is $ (Round to the nearest dollar) You recelve a $2,000 check from your grandparents for graduation. You decide to save it toward a down payment on a house. You invest it eaming 8% per year and you think you will need to have $4,000 saved for the down payment. How long will it be before the $2,000 has grown to $4,000 ? To double the money you received from your grandparents, it will take years. (Round to one decimal place.)

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