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?

Respuesta :

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.