Paying off a mortgage twice as fast? My brother has a 30 year fixed mortgage. He pays monthly. Every month my brother doubles his principal payment (so every month, he pays a little bit more, according to how much more principal he's paying).
He told me he'd pay his mortgage off in 15 years this way. I told him I though it'd take more than 15 years. Who's right? If I'm right (it'll take more than 15 years) how would I explain this to him?
CLARIFICATION: He doubles his principal by looking at his statement and doubling the "amount applied to principal this payment" field.

Let's look at two scenarios: two months of payment $P$ vs. one month of payment $2P$. Start with the second scenario. Assume the total amount to be payed is $X$ and the rate is $r > 1$, the total amount to be payed after one month would be $$r(X-2P).$$ Under the first scheme, the total amount to be payed after two months would be $$r(r(X-P)-P) = r(rX - (1+r)P).$$ Most of the time, $X$ is much larger than $P$, and so $X-2P$ is significantly smaller than $rX - (1+r)P$ (remember $r \approx 1$). So it should take your brother less than 15 years.
Note I first subtract the payment and then take interest, but it shouldn't really matter.
This all assumes the payments are fixed, but looking at the other answers this is not really the case... I guess my banking skills are lacking. Too young to take loans.
