There is in Brazil a negotiable financial instrument
called a "consórcio não contemplado", a contract 
between a bank (or similar financial institution) and
a consumer (typically a home buyer). The contract
provides for the bearer (the consumer) to make a fixed
number (generally 140) monthly payments to the bank, 
and for the bank to provide a lump sum payment to the
bearer at some time between the 1st and the last month
of the contract. Both the payment and the principal are
adjusted for inflation monthly. The time of disbursement
of principal by the bank is chosen by non-replacement
lottery, which guarantees a "1 in N" chance of being chosen,
N being the number of payments left. To keep bank´s lottery
pickings honest, pools of 140 consumers are drawn and made
public at the  beginning of the contract, so it is easy to
audit and verify someone is being chosen each and every month
from the prearranged group. All 140 payments are due each
month regardless of when a consumer is chosen to receive the
principal. Each payment also has a built-in administrative
fee of roughly 0.333% of the principal value, per month,
which is effectively a real interest rate of 4% per year
charged by the bank.

The contract described is fully negotiable, it can be bought
and sold between consumers directly before or after it is
randomly chosen (when it becomes a "consórcio contemplado"
and the principal can be used to purchase real estate from
a third party). Note that each contract is guaranteed the
same inflation-adjusted payout, only the timing is random.
That reduces the bank´s capital requirements and spreads
certain risks.

My question is, please provide a formula to calculate the
fair value of one such contract, given the mentioned variables:
* total number of payments contracted (almost always 140)
* number of payments left
* principal amount
* payment amount
* inflation rate (assume this is always constant, for simplicity)
* prevailing return rate on alternative investments

The administrative fee is not a variable, since it can be
derived when the above are given.

This will require some knowledge of bond pricing and option
pricing theory.

The formula must be in Excel format.

If the amount offered for this question is not adequate,
please indicate an amount for which you would perform the
research.

Thanks!