Question

a.	What is the amount of the annuity purchase required if you wish to receive a fixed payment of $230,000 for 20 years? Assume that the annuity will earn 13 percent per year. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Present value

$

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 13 percent. The payments are to begin at the end of the current year. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Annual cash flows

$

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 13 percent. The payments are to begin at the end of six years. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Annual cash flows

$

Answer 1

a). PVA = Annuity x [{1 - (1 + r)^-n} / r]

= $230,000 x [{1 - 1.13^-20} / 0.13]

= $230,000 x [0.9132 / 0.13] = $230,000 x 7.0248 = $1,615,692.86

b). Annuity = [PVA x r] / [1 - (1 + r)^-n]

= [$1,400,000 x 0.13] / [1 - 1.13^-20] = $182,000 / 0.9132 = $199,295.30

c). In this case, the first annuity is to be received six years from today. The initial sum today will have to be compounded by five periods to estimate the annuities:

PVA = Annuity x [{1 - (1 + r)^-n} / r]

$1,400,000(1 + 0.13)^5 = X [{1 - (1/(1 + 0.13)^14)}/0.13]

$2,579,409.25 = X[0.8193 / 0.13]

X = $2,579,409.25 x [0.13 / 0.8193] = $409,268.41