Question

A. What is the amount of the annuity purchase required if you wish to receive a fixed payment of $260,000 for 15 years? Assume that the annuity will earn 13 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 13 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 13 percent. The payments are to begin at the end of five years.

Answer 1

A)

N = 15

I/Y= 13

PMT = 260,000

FV = 0

CPT PV

PV = -1,680,218.494

The amount of the annuity purchase required is $1,680,218.494

B)

N = 15

I/Y = 13

PV = -1,600,000

FV = 0

CPT PMT

PMT = 247,586.8475

The annual cash flows are $247,586.8475

C)

PV at the end of one year before the first payment = PV4 = 1,600,000*(1 + 0.13)^4 = 2,608,757.776

N = 15

I/Y = 13

PV = -2,608,757.776

FV = 0

CPT PMT

PMT = 403,683.821

The annual cash flows are $403,683.821 which begin at the end of year 5

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