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Suppose that you will receive annual payments of $11,000 for a period of 10 years. The first payment will be made 5 years from now. If the interest rate is 5%, what is the present value of this stream of payments? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Present value You believe you will need to have saved $400,000 by the time you retire in 40 years in order to live comfortably. If the interest rate is 5% per year, how much must you save each year to meet your retirement goal? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual savings What is the value of a perpetuity that pays $100 every 6 months forever? The interest rate quoted on an APR basis is 6.8%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Value of a perpetuity Good news: You will almost certainly be a millionaire by the time you retire in 40 years. Bad news: The inflation rate over your lifetime will average about 2.9%. a. What will be the real value of $1 million by the time you retire in terms of today's dollars? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Real value b. What real annuity (in today's dollars) will $1 million support if the real interest rate at retirement is 2.1% and the annuity must last for 10 years? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Real annuity