to repay this sum in 20 oqual annual installments that include both principal and 15 percenm interest on the declining balance. How large will the annual payments be? 6-26. Annuity payments) To buy a new house, you must borrow S150,000. To do this you take out a $150,000, 30-year, 10 percent moetgape. Your moetgage payments, which are made at the end of each year (one payment each year), include both pein- cipal and 10 percent interest on the declining ballance. How large will your annual payments be? 6-27. (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 paymenes (the initial two payments, with the first CHAPTER & The Time Value ot Money 183 coming after six months have passed, and the second one coming at the end of the first year) goes toward paying interest, rather than principal? 628. (Related to Checkpoint &2 on page 165)(Present value of annuity payments) The dale lotery's million-dollar payout povides for S1 million to be paid over the course of 19 ycars in amounts of $50,000, The first 550,000 payment is male immediately and the 19 remaining If 10 percent is the discount rale, what is the present value of this stream of cash flows? Ir 20 pencet is the discount rale, what is the peesent value of the cash flows? $50000 payments oocur at the end of each of the next 19 years 6-29. (Future value of an annuity) Find the future value at the end of Year 10 ofan annuity that pays $1,000 per year for 10 years compounded annually at 10 percent What would be the future value of this annuity if it were compounded annually at 15 percent? Present value of an annuity due, Determine the present value of an annuity due of $1,000 per year for 10 years discounted back to the present at an annual rate of 10 percent. What would be the present value of this annuity due if it were discounted at an annual ae of 15 percent? 6-31. (Present value of an annuity) Detemine the present value of an ordinary annuity of earms 10 percent Assume that the first cash 1,000 per year for 10 years, assuming flow from the annuity comes at the end of Year 8 and the final payment a the end of Year 17. That is, no payments are made on the annuity at the end of Years I through 7 Instead, annoal payments are made at the end of Years 8 through 17 6-32. (Components of an annuity payment) You take out a 25-year mortgage for 300,000 to buy a new house. What will your monthly payments be if the imer- est rate on your mortgage is 8percent? Use a spreadsheet to calculate your answer Now, cakculate the portion of the 48th monthly payment that goes toward inmerest and principal 6 (Comprehensive problem) Over the past few years, Microsoft founder Ball Gates's net worth has flactualed between $20 and S130 billson. In carly 2006, it was about 26 billion -afler he reduced his stake in Miecrosoft from 21 percent to around 14 percent by moving billions into his charitable foundation. Let's see what Bill Gales can do with his money in the follkowing problems a. Manhattan's mative tribe sold Manhattan Island to Peter Minuit for $24 in 1626 Now, 387 years later in 2013, Bill Gates wants to buy the island from the "current natives." How much would Bill have to pay for Manhattan if the "current natives want a 6 percent annual return on the original $24 purchase price b. Bill Gales decides to pass on Manhattan and insicad plans to buy the city of Seat- le, Washington, for SS0 billion in 10 years. How much would Bill have to invest today at 10 percent compounded annually in order to purchase Seattle in 10 years? e. Now assume Bill Giates only wants to invest half his net worth today, $13 bil- lion, in onder to buy Seattle for $30 billion in 10 years. What annual rate of return would he have to earn in order to complete his purchase in 10 years? d Inslcad of buying and running large cities, Bill Getes is comadering quitting the rigors of the business world and retiring to woek on his golf game. To fund is retirement, Bill would invest his $20 billion fortune in safe investments with an expected annal rabe of retum of 7 percent. He also wants to make 40 oqual annual wihdrawals from this retirement fund beginning a year from today, running his retirement fund to 50 at the end of 40 years. How much can his annual withdrawal be in this case