Answer:
Instructions are listed below.
Step-by-step explanation:
Giving the following information:
Alex Meir recently won a lottery and has the option of receiving one of the following three prizes:
(1) $86,000 cash immediately
(2) $32,000 cash immediately and a six-period annuity of $9,200 beginning one year from today
(3) a six-period annuity of $17,400 beginning one year from today.
1)
A) i= 0.06
i) PV= 86,000
ii) First, we need to calculate the final value of the annuity:
FV= {A*[(1+i)^n-1]}/i
A= annual pay
FV= {9,200*[(1.06^6)-1]}/0.06 + [(9,200*1.06^6)-9,200]= 68,023.31
PV= FV/(1+i)^n= 68,023.31/1.06^6= 47,953.75 + 32,000= $79,953.75
ii) FV= {17,400*[(1.06^6)-1]}/0.06 + [(17,400*1.06^6)-17,400]= 128,652.77
PV= 128,652.77/1.06^6= $90,695.13
B) The option with the higher present value is option 3. Therefore, it is the best option.
2) Weimer will make annual deposits of $170,000 into a special bank account at the end of each of 10 years beginning December 31, 2016.
Assuming that the bank account pays 7% interest compounded annually.
FV= {A*[(1+i)^n-1]}/i
FV= {170,000*[(1.07^10)-1]}/0.07
FV= $2,348,796.15