she is making 15000 per month in the first yer.
in the second year, and every year after that, she is making an additional 1500 per month.
her expenses in the first year are 13000 per month.
in the second year, and every year after that, her expenses per month are an additional 900 per month.
i translated this to yearly salary and yearly expenses.
15000 per month * 12 = 180,000 per year.
1500 per month * 12 = 18,000 per year.
13000 per month * 12 = 156,000 per year.
900 per monmth * 12 = 10,800 per year.
the equation for her salary growth is S = 180,000 + 18,000 * x.
the equation for her expenses is E = 156,000 + 10,800 * x.
x is the number of years.
the equations for her savings for each year is V = S - E.
this becomes V = 180,000 + 18,000 * x - 156,000 - 10,800 * x.
combine like terms to get V = 24,000 + 7,200 * x
if her savings are going to be 20,000 per month, then her savings per year will be 20,000 * 12 = 240,000 per year.
you want to know how many years before her savings per month = 20,000.
this should be equivalent to asking how many years before her savings per month = 240,000.
replace V with 240,000 and the equation of V = V = 24,000 + 7,200 * x becomes 240,000 = 24,000 + 7,200 * x.
solve for x to get x = (240,000 - 24,000) / 7,200 = 30.
if correct, it would take 30 years for her savings per month to be equal to 20,000.
i used excel to confirm that this is true.
here's two displays from the excel analysis.
the first shows the first two years.
the second shoes the last two years.
the monthly savings becomes 20,000 in the thirty first year.
the thirty first year is thirty years after the first year.
this is based on my interpretation of your problem.
if my interpretation is in error, then please be more specific about what your interpretation of the problem is.