Question

Value of an annulity versus a single amount Personal Fnance Problm Assume that you just won the stae ottery Your price can be tken olthar in the 900,000 over 25 years) or as a single amount of $411,000 paid inmediately aif you expect to be able to earn 8% anually on your mestne s over the next 2S yenigo ng taxes ar dote, orsiserat ons b would your decisin in part a change you could earn 10% rather than 8% on your investments over the next 25 years? why? c. On a strictly economic basis at approximately what eainings rate would you be form of $36,000 at the end of each of the next 25 yearshat is indifierent between the two plans? vakues of these aternives Although the total nominal dollar amount of the anuity is much larger than the single payment, the former is not nacessarly a better a. To decide which alternative to take, you need to compare the these alternatives choice due to the different Siming of cash flows A way to make a meaningful comparison of the two abernatives is to compare their present values If you take the price as an annuly, he present value of the 25-year ordinay annulity is Round to the nearest cent If you take the prize as a single amount,the present value of the lump sum is Round to the nearest do) Which atemative should be chosen? (Select the best answer below) O Annual payments, because the present value is greater O Lump sum, because the present vakue is greater b. If you earned 10% rather than อ% on your investment, the present value of h. Syear ondinry nnnuty s s[] Rundio he intret iii) Which altermative should be chosen? (Select the best answer below )

Answer 1

a. if I will get an interest of 8% per year upto 25 years, then if I take $411,000 now, I will get an interest income for every year is

= $411,000*0.08= $32,880

32880*25= $822,000

plus principal amount is= 822,000+411000= $1,233,000

if I accept the annual payment of $36,000 it is going to become $900,000 only.

Hence, it is better to take lumpsump amount of $411,000 is good opportunity to me.

the present value of annuity is at 10% interest rate is= 9.0770