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

Question

Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 20-year annuity is $1.7 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))

Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 20-year annuity is $1.7 million and the annuity earns a guaranteed annual return of 10 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))

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))

Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 20-year annuity is $1.7 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))

Explanation / Answer

Answer a.

Present Value of annuity = $1,700,000
Period of annuity = 20 years
Annual Interest Rate = 10%

Present Value of annuity = Annual Cash flows * PVA of $1 (10%, 20)
$1,700,000 = Annual Cash flows * (1 - (1 / 1.10)^20) / 0.10
$1,700,000 = Annual Cash flows * 8.51356
Annual Cash flows = $199,681.45

So, Annual cash flows is $199,681.45

Answer b.

Present Value of annuity = $1,700,000
Period of annuity = 20 years
Semi-annual period of annuity = 40
Annual Interest Rate = 10%
Semi-annual Interest Rate = 5%

Present Value of annuity = Semi-annual Cash flows * PVA of $1 (5%, 40)
$1,700,000 = Semi-annual Cash flows * (1 - (1 / 1.05)^40) / 0.05
$1,700,000 = Semi-annual Cash flows * 17.15909
Semi-annual Cash flows = $99,072.85

So, Semi-annual cash flows is $99,072.85

Answer c.

Annual payment = $200,000
Period of annuity = 20 years
Annual Interest Rate = 10%

Present Value of annuity = Annual Cash flows * PVA of $1 (10%, 20)
Present Value of annuity = $200,000 * (1 - (1 / 1.10)^20) / 0.10
Present Value of annuity = $200,000 * 8.51356
Present Value of annuity = $1,702,712.00

So, Present Value of annuity is $1,702,712.00

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