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10. You are offered an annuity that will pay you $200,000 once every year, at the end of each year, for 25 years (i.e. the first payment will arrive one year from now, the last payment will arrive 25 years from now). Suppose your annual discount rate is i=5.25%, how much are you willing to pay for this annuity? Hint: this is the same as the present value of an annuity.

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Answer:

PV= $2,749,494

Explanation:

Giving the following information:

Cash flow= $200,000

Number of periods= 25

Interest rate= 5.25%

First, we need to calculate the future value using the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual cash flow

FV= {200,000* [(1.0525^25) - 1]} / 0.0525

FV= $9,881,102.14

Now, the present value:

PV= FV/(1+i)^n

PV= 9,881,102.14 / (1.0525^25)

PV= $2,749,494

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