calculate the cash value of a financed asset that is paid in the following way: an initial payment of 500,000, in month 2 a payment equal to half its value, in month 7 a payment equal to a third of its value and in month 10 200,000, the interest rate is 3% and focal date in month 4.
Using the value equation I get:
$$P(1+0.03)^4 = 500000(1+0.03)^4 +\frac{P}{2}(1+0.03)^2+\frac{\frac{P}{3}}{(1+0.03)^3} + \frac{200000}{(1+0.03)^6}$$
solving for P I get:
$$P = 3,175,005$$
Did I set up the value equation correctly? Is that The correct value of the asset?
Note:
Focal date:A specific time chosen to compare the time value of one or more dated sums of money.
Value equation is: $$Income_{focaldate} = Expenses_{focaldate}$$
the formula for the future value of money (compound) where F is future, P is present, i is the interest rate and T is the period :
$$F = P(1+i)^T$$
and the Present value
$$P = \frac{F}{(1+i)^T}$$
You have set up the equation for $P$ (valuation at start of period) properly, but I get a different answer for $P$ using your equation, $\approx 2.5$ million, so please recheck your computation.
The other point is that if the cash value is to be computed for the focal date, the answer will be the value at the focal date,ie $P(1.03)^4$, not $P$