Question

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

Answer 1

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