Question

a. What is the amount of the annuity purchase required if you wish to receive a fixed payment of $220,000 for 25 years? Assume that the annuity will earn 11 percent per year.
b. Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 25-year annuity is $1.1 million and the annuity earns a guaranteed annual return of 11 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 25-year annuity is $1.1 million and the annuity earns a guaranteed annual return of 11 percent. The payments are to begin at the end of six years.

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

Answer 1

a. we can use financial calculator for calculation of present value of annuity with below key strokes:

N = no. of years = 25; PMT = payment = $220,000; I/Y = interest rate = 11%; FV = future value = $0 > CPT = compute > PV = present value = $1,852,783.83

the amount of the annuity purchase required is $1,852,783.83.

b. we need to calculate payments.

N = no. of years = 25; PV = present value = $1,100,000; I/Y = interest rate = 11%; FV = future value = $0 > CPT = compute > PMT = payment = $130,641.27

the annual cash flows (annuity payments) from a fixed-payment annuity is $130,641.27.

c. first we need to calculate future value of $1,100,000 at the end of six years.

Future value = present value*(1+interest rate)no. of years = $1,100,000*(1+0.11)6 = $1,100,000*1.116 = $1,100,000*1.870414552161 = $2,057,456.0073771‬

now we can calculate annual cash-flows using present value of $2,057,456.0073771‬ for remaining 19 years (25 - 6).

N = no. of years = 19; PV = present value = $2,057,456.0073771; I/Y = interest rate = 11%; FV = future value = $0 > CPT = compute > PMT = payment = $262,454.24

the annual cash flows (annuity payments) from a fixed-payment annuity is $262,454.24.