\nI was looking at the formula for the periodic payment of a mortgage:\n
\nP=(-1(r\/n))*L*(1+r\/n)^(nt)\/(1-(1+r\/n)^(nt))\n<\/p>\nwhere\n
P=payment<\/p>\n
r=rate<\/p>\n
n=payments per year (and compounding periods per year as well)<\/p>\n
t=years<\/p>\n
Specifically I was wondering if it can be rendered, algebraically, to be a formula for r, the rate. However, I don’t think it can.<\/p>\n
To “get r by itself”, you’d have to take the (nt)th<\/sup> root of the terms (1+r\/n)^(nt). Yet, there is also a term on the top, r\/n, which won’t root out at the same time. Therefore, I suspect that formula can’t be solved for r.<\/p>\n “But Jack,” someone might say, “why would you even think about that? Everyone uses financial calculators or computer apps to calculate such a value.” Yes, true: the idea is academic, which is exactly why I bring it up:)<\/p>\n Source:<\/p>\n thebalance.com<\/a><\/p>\nJack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.\n","protected":false},"excerpt":{"rendered":" Self-tutoring about financial math: the tutor mentions the mortgage interest rate. I was looking at the formula for the periodic payment of a mortgage: P=(-1(r\/n))*L*(1+r\/n)^(nt)\/(1-(1+r\/n)^(nt)) where P=payment r=rate n=payments per year (and compounding periods per year as well) t=years Specifically …<\/p>\n