Question

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.

Answer 1

Given:

Annuity payments = $200,000

Number of periods = 25 years

Discount rate = 5.25%

You are asked to compute the amount you are willing to pay now for this annuity. This can be computed by finding the present value of the annuity. The maximum amount you are willing to pay for this annuity will be the present value of this annuity.

Here, the payments are made at the end of each year, so this is an ordinary annuity.

The formula for computing the present value of ordinary annuity is:

P [ (1 - (1 + r)^-n) / r]

P = Periodic payment = $200,000

r = Rate on interest or Discount rate = 5.25% ie, 0.0525

n = Number of periods = 25

Substituting the values in the formula we get,

200000 [ (1 - (1 + 0.0525)^-25) / 0.0525 ]

= 200000 [ (1 - (1.0525)^-25) / 0.0525 ]

= 200000 [ (1 - 0.278257) / 0.0525 ]

= 200000 [ 0.7217422 / 0.0525 ]

= 200000 * 13.74747

= 2,749,494

Present value of annuity = $2,749,494

Therefore, the amount you would be willing to pay for this annuity is $2,749,494