You are comparing two annuities with equal present values. The applicable discount rate is 6.5 percent. One annuity will pay $2,000 annually, starting today, for 20 years. The second annuity will pay annually, starting one year from today, for 20 years. What is the annual payment for the second annuity?

Answer:

Present value of both annuities are equal.

PV of annuity 1 that pays today can be calculated using PV formula in excel or calculator

PV = pv(rate = 6.5%, nper = 20, pmt = 2000, fv = 0, 1) = $23,469.42

Now, the present value of the second annuity is equal to $23,469.42 and annual payment can be calculated using PMT formula in excel or calculator

Annual Payment = PMT(rate = 6.5%, nper = 20, pv = 23,469.42, fv = 0, 0) = $2,130 is the annual payment of second annuity.

Other way to calculate it is - Annual Payment = 2,000 x (1 + 6.5%) = $2,130. The only difference between the two annuities is in the first cash flow.