a. Calculate the annual cash flows (annuity payments) from a fixed-payment annui

Question

a. Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 20-year annuity is $1 million and the annuity earns a guaranteed annual return of 10 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 b. Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 20-year annuity is SI million and the annuity earns a guaranteed annual return of 10 percent. The payments are to begin at the end of five years. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) Annual cash flows c. What is the amount of the annuity purchase required if you wish to receive a fixed payment of $200,000 for 20 years? Assume that the annuity will earn 10 percent per year. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) Present value

Explanation / Answer

Solution:

Future Value = Present Value * (1+return)period

Future Value = 1,000,000 * (1+10%)5

                   = 1,000,000 * 1.61051

                   = $1,610,510.

Future alue 5 years from today = Present value of annuity at 5 years from today = $1,610,510.

Present Value of Annuity = Annuity * Annuity Discount Factor

Annuity = Present Value of Annuity / Annuity Discount Factor (10%, 20 years).

Annuity = 1,610,510 / 8.51356 = 189.169.98.

Annuity = $189.169.98.

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