$\displaystyle P=A(((1+re)^1/12 -1) / (1 - (1+re)^-n)))$

Consider a €100,000 mortgage borrowed for a period of 40 years.

How many years is half the oroiginal mortgage paid?

Interest rate = 4%

n = 40 years

re= .04 therefore r = .039 as $\displaystyle (1+ r/12)^12 = 1 + re$

the problem i have is, P is meant to equal €413.50 but i just cant seem to get it to work out like that, the P formula is giving me minus answers and stuff.

By the way in the P formula it is 1+re to the power of 1/12 and the other 1+re is to the power of -n

Please help!!