The exact calculation for a montly repayment of any loan with an interest of X% APR
First we calculate the monthly interest as the APR stand for Annual (yearly)
-ⁿ√ (1+ i )
example: for a 8%APR, the interest per month is:
-12↑√ (1+0.08) = 1.00643403 or 0.643403% per month
where n is number of repayment periods (12 months per year) and i stand for interest
We are now ready to calculate any repayment loan or mortgage over a certain period of time
i / (1 – ((1 + i )power of -n))
example: the monthly payment for a repayment mortgage of £450,000 over 25 years at 8% APR will be : (n=300 - 25years multiple by 12months)
0.00643403 / (1 – ((1+0.00643403)power of-300)) = 0.00753415 X 450,000 = £3390.36
And an interest only mortgage will be:
0.00643403 X £450,000 = £2895.31
It is a rather long process hence the bank clercks have a ready-made printed table at hand.
Hope it does answer your question!!!