Question

a. What is the amount of the annuity purchase required if you wish to receive a fixed payment of $250,000 for 15 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 15-year annuity is $1.6 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 15-year annuity is $1.6 million and the annuity earns a guaranteed annual return of 10 percent. The payments are to begin at the end of eight years.

(For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))
  

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= 250000*((1-(1+ 10/100)^-15)/(10/100))

PV = 1901519.88

b

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

C = Cash flow per period

i = interest rate

n = number of payments

1600000= Cash Flow*((1-(1+ 10/100)^-15)/(10/100))

Cash Flow = 210358.04

c

FV at end of year 9

Future value = present value*(1+ rate)^time

Future value = 1600000*(1+0.1)^9

Future value = 3772716.31

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

C = Cash flow per period

i = interest rate

n = number of payments

3772716.31= Cash Flow*((1-(1+ 10/100)^-15)/(10/100))*(1+10/100)

Cash Flow = 450921.15