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sent Value and Discounting,How much would an investor have to set aside today in order to have $20,000 five years from now if the current rate is 15%?,$20,000,PV,In the multiperiod case, the formula for the present can be written as:,How Long is the Wait?,If we deposit $5,000 today in an account paying 10%, how long does it take to grow to $10,000?,What Rate Is Enough?,Assume the total cost of a college education will be $50,000 when a child enters college in 12 years. His/Her parents have $5,000 to invest today. What rate of interest must his/her parents earn on their investment to cover the cost of the child’s education?,About 21.15%,At 9 percent interest, how long does it take to double your money? To quadruple it?,Have a try!!!,Multiple Cash Flows,Consider an investment that pays $200 one year from now, with cash flows increasing by $200 per year through year 4. If the interest rate is 12%, what is the present value of this stream of cash flows? If the issuer offers this investment for $1,500, should you purchase it?,Present Value Cost → Do Not Purchase,The present value of the following cash flow stream is $6,453 when discounted at 10 percent annually. What is the value of the missing cash flow? Year 1 Cash flow $1,200 Year 2 Cash flow ? Year 3 Cash flow $2,400 Year 4 Cash flow $2,600,Have a try!!!,4.3 Compounding Periods,Compounding an investment m times a year for T years provides for future value of wealth:,For example, if you invest $50 for 3 years at 12% compounded semiannually, yo