Reconcile two different ways to calculate a discount rate for present value

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. (Happy)

I have a single data point that a dollar today will be worth $0.22 after 24 months. Given the present value equation: PV_{i} = 1 / ( 1 + *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 (*r* in the PV equation) is 0.024316.

or

B) By plugging in 0.22 for PVi and 24 for *i*, we can rewrite the PV equation to solve for *r* as 1 - (1 / 0.22)^{(1/24) }= 0.06512, thus the discount rate (*r* in 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?

Re: Reconcile two different ways to calculate a discount rate for present value

So you are expecting a sharp deflation after many years of inflation? Or do you mean an **increase** of $0.22 so that, after two years, a dollar will be worth $1.22?

Re: Reconcile two different ways to calculate a discount rate for present value

I suppose it most closely resembles inflation. So $1 in month 24 is worth $0.22 today.

Re: Reconcile two different ways to calculate a discount rate for present value

Quote:

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 (r in the PV equation) is 0.024316.

you are not given a rate of 78% spread over 24 months. Your 0.22 will accumulate to $1. that is a accumulation of about 400% over 24 months.

you have solved for the interest rate in b.

Re: Reconcile two different ways to calculate a discount rate for present value

Quote:

Originally Posted by

**odonnellphil** I suppose it most closely resembles inflation. So $1 in month 24 is worth $0.22 today.

Why in heck don't you use something CLEAR...

You are asking about PV calculations, not inflation or whatever, right?

$85 in a savings account accumulates to $100 after 2 years, at rate of P% compounded annually.

What is P?

You have 2 ways of calculating P? ... or what are you asking?