How do mortgage calculators compute?

cafc

Can anyone tell me how mortgage calculators work?
I have a £41000 repayment mortgage at 5% over 20 years.
I have entered these figures into various calculators & they all calculate approx £270.

How much of the £270 is interest & how much capital?
How will this split differ over the course of the 20 years?

Thanks in anticipation.
cafc

payless

I have seen some clever people post calculations/ spreadsheets- in fact there may be examples in templates of your own spreadsheet.

Results depend on various factors ( daily interest being one)

I have pulled out an example ( I'm not that clever with spreadsheets- but pay for a sourcing/ illustration program) on the terms you mention ( assuming daily interest)

Unfortunately I can't paste it all here
BUT example on a monthly cost of £270.58

the payments ( assuming constant interest rate) and no other changes would
remain the same , and less would be interest element , as more of the payment would go to capital


in
year 1 you would pay about £1225 capital
Year 5 £1495
Yr 10 £1919
yr 15 £2463
yr 20 £3161

hope this helps

jay7_2

Could we say that typically about a half of the repayments is capital repayments and the other half is interest repayments during the first year and the proportion changes (more capital repayments) in later years? Is there a table or a graph showing the typical proportion of capital / interest repayments available somewhere in the Internet? Cheers.

payless

the interest rate, term and daily / annual would all be factors

in the example shown its 38% capital (average) during the first year

takethemoney

cafc,
if your really keen to understand your mortgage this is an excellent site;
http://www.mortgagesexposed.com/
it explains all you need to know

david78

At the start of the mortgage most of the repayment is interest and very little is capital. At the end it reverses, most is capital, and little is interest.

You can calculate the amounts as follows (I assume daily interest here).

Let

r = average interest rate as a fraction (so 6% means r = 0.06)
m = term of mortgage IN MONTHS (so m = 300 for 25 year loan)
n = time into mortgage IN MONTHS (so n = 84 for seven years)
B0 = initial mortgage amount
Bn = amount of principal owing after n months
P = monthly payment required (=Pi+Pc) constant throughout term
Pi = amount of P which is interest after n months
Pc = amount of P which is capital after n months

(be sure to put m and n in months!)

Technically r is a "nominal rate". Calculate the monthly rate using:

rm = r/12

Your monthly payment should be:

P = B0*rm/((1+rm)^m-1) + B0*rm

You can get the split of Pi and Pc after n months using:

a = (1+rm)^m/((1+rm)^m-1)
b = (1+rm)^(m-n)/((1+rm)^(m-n)-1)
Bn = B0 * (a/b)
Pi = Bn*rm
Pc = Bn * rm/((1+rm)^(m-n)-1)
P = Pi + Pc

The last equation should always give you the same value. The monthly repayment is constant, but Pi decreases and Pc increases. Its relatively easy to put these formulae in Excel and plot a graph of Pc and Pi vs n.

For example, with an initial mortgage of £100,000 and an interest rate of 6% over 25 years you get a monthly payment of £644 (initially £500 of this is interest and £144 is capital). With a little work in Excel you get this graph . (I haven't done your actual example, you can do it easily enough using the formulae above.)

jay7_2

Thanks for the detailed answer, david78.