A financed machine is acquired and it is agreed to cover in three payments of $ 60,000, $ 80,000 and $ 100,000 in months six, eight and twelve respectively. Find the value of the spot price knowing that the financing contemplates an interest rate on the balance of 2.5% per month for the first six months and 9% quarterly thereafter.

What continuously capitalizable interest rate is equivalent to the nominal monthly interest rate that converts today\'s $ 310,000 to $ 787,580 in twenty-five months?