what is the present value of the following annuity 2095 ever

what is the present value of the following annuity? 2095 every year at the end of the year for the next 13 years, discounted back to t he present at 7.42 percent per year compounded annually

Solution

Formula for PV of annuity is:

PV = P x [1-(1+r)^-n/r]      

P = Periodic cash flow = $ 2,095

r = Rate per period = 7.42 % or 0.0742 p.a.

n = Numbers of periods = 13

Substituting all the values in above formula we get PV as:

PV = $ 2,095 x [1-(1+0.0742)^-13/0.0742]

= $ 2,095 x [1-(1.0742)^-13/0.0742]

= $ 2,095 x [(1-0.3943602)/0.0742]

= $ 2,095 x (0.6056398/0.0742)

= $ 2,095 x 8.16226149

= $ 17,099.9378 or $ 17,099.94

Present value of annuity is $ 17,099.94