f An investment will pay you 5000 in 9 years and it will als

f. An investment will pay you $5,000 in 9 years, and it will also pay you $200 at the end of each of the next 9 years (years 1 thru 9). If the annual interest rate is 5%, how much would you be willing to pay today for this type of investment? (Round your intermediate calculations and final answer to the nearest whole dollar) Present value g. A college student is reported in the newspaper as having won $5,000,000 in the Kansas State Lottery. However, as is often the custom with lotteries, she does not actually receive the entire $5.0 million now. Instead she will receive $250,000 at the end of the year for each of the next 20 years. If the annual interest rate is 5%, what is the present value (today\'s amount) that she won? (ignore taxes). (Round your answer to nearest whole dollar.) Present value $3,115,550

Solution

Question (f) Computation of the Present Value Annual Amount received =$200 Annual interest rate =5% Amount received at the end of the 9th year =$5000 Present Value factor at5% at 9 years =0.644609 Present Value Annuity factor at5% at 9 years =7.107822 Present Value =Annual receipt *Present Value Annuity factor at 5% for 9 years + Amount received at the end of the 9th year *Present Value factor at5% at 9 years Present Value =($200*7.107822) +($5000*0.644609) =$1421.56+$3223.05 =$4644.60 Amount willing to pay for this Investment today =$4645 (rounded off) Question no(g) Present Value of lottery =Annual receipt *Present Value Annuity factor at 5% for 20years Annual receipt =$250,000 number of receipts =20 years Present Value Annuity factor at 5% for 20years =12.4622 present Value of Lottery =$250,000*12.4622 =$3,115,550