Question

a. What is the amount of the annuity purchase required if you wish to receive a fixed payment of $240,000 for 20 years? Assume that the annuity will earn 10 percent per year.
b. Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 20-year annuity is $1.4 million and the annuity earns a guaranteed annual return of 10 percent. The payments are to begin at the end of the current year.
c. Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 20-year annuity is $1.4 million and the annuity earns a guaranteed annual return of 10 percent. The payments are to begin at the end of six years.

Answer 1

a

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 240000*((1-(1+ 10/100)^-20)/(10/100))

PV = 2043255.29

b

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

1400000= Cash Flow*((1-(1+ 10/100)^-20)/(10/100))*(1+10/100)

Cash Flow = 149494.07

Please ask remaining parts separately, questions are unrelated. I have done one bonus