You just purchased an annuity that will pay you $24,000 a year for 25 years, starting today. what was the purchase price if the discount rate is 8.5 percent?

This problem is an example of an Annuity due problem. To solve this problem, let us recall that the formula for Annuity due is:

PV = A [[1 – [1 / (1 + r)^n]] / r] * (1 + r)

Where the variables are,

PV = Present value or the purchase price today

A = Annuity value = $24,000

r = Discount rate = 8.5 % = 0.085

Substituting the given values to the equation:

PV = 24,000 [[1 – [1 / (1.085)^25]] / 0.085] * (1.085)
PV = 24,000 * 11.104097

PV = $266,498.3279

Therefore the purchase price is about $266,498.

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