# Mortgage question

Assume i take the mortgage out over 25 years: using the mortgage payment formula below:

$Monthly\ payment\ = L\ [{\dfrac{x(1+x)^n}{(1+x)^n -1} }]$

where L is the loan value, x is the interest % in month and n is the number of months

In my scenario if my interest payment is 3% a year, on a £330k loan over 25 years this would equal:

$£330,000[{\dfrac{0.0025(1.0025)^{(25*12)}}{(1.0025)^{(25*12)} -1} }] = £1564$ a month

Therefore in 5 years i would have paid off £93,893 of the loan including interest over those 5 years.

My question is if i sell the house at the end of the 5 year period - what amount of the mortgage would i have to pay there and then, as the interest is calculated year on year i.e. paying it off in advance would save you the interest payments over the remainder of those years.

Using typical mortgage calculators online if i figure out the balance of the mortgage left over it will give me that balance over the remaining 20 years. How do i find out the real time value of that debt if i wanted to pay it off there and then?

• You can find the balance after five years using the Mortgage tab in the PayoffDebt.xlsx spreadsheet at commonsensemathematics.net/spreadsheets - check that it's the same formula you are using. – Ethan Bolker Oct 30 '17 at 23:18

$Monthly\ payment\ = L\ [{\dfrac{x(1+x)^n}{(1+x)^n -1} }]$
therefore $L\ = {\dfrac{(1+x)^n -1}{x(1+x)^n} }(Monthly\ payment)$
use the Monthly payment you have already have (and rate) and use $240$ to represent the number of payments left after $5$ years
or $L = \dfrac{(1.0025)^{300} -(1.0025)^{60}}{(1.0025)^{300} -1}330,000$