A colleague and I are in disagreement on the correct way to calculate a discount rate for a present value equation and would like an opinion from some more knowledgeable folks.

I have a single data point that a dollar today will be worth $0.22 after 24 months. Given the present value equation: PV= 1 / ( 1 +_{i}r) ^i...

A) That is a rate of 78% over 24 months, so the monthly compounded rate is (1+.78)^{(1/24)}- 1 = 0.024316, thus the discount rate (rin the PV equation) is 0.024316.

or

B) By plugging in 0.22 for PVi and 24 fori, we can rewrite the PV equation to solve forras 1 - (1 / 0.22)^{(1/24) }= 0.06512, thus the discount rate (rin the PV equation) is 0.06512.

Both these approaches seem valid to me, but obviously they will result in very different answers for Present Value. A) would give a PV_{24}of 0.56 per dollars and B) gives a value of 0.22 per dollar.

Can anyone help me figure out which approach is the correct one?