What have you tried? The only dilemma on this one is the lack of perfect synchronization of the payments and the interest crediting. What would be most useful is a quick equivalency.
There you go, an equivalent annually compounded rate.
Scope out the value:
I do not get the answer you provided. The given answer ignores the semi-annual compounding and simply is incorrect.
Note: This is a nice number, but it really does not answer the question. If you paid EXACTLY what the machine is worth, there would be no benefit to buying it. If you do nothing, your prospects are zero. If you buy for exactly what it will earn you, your prospects are zero. A reasonable price would have to be something less than the value of the business it can generate. Why go into a 10-year venture with no expectation of profit?