how to calculate interest?

[Tjalfe]

so out of curiosity, I decided I wanted to make up a spreadsheet with our mortgage calculations etc. I got what I thought was the right formular going, but for some reason the bank comes up with different numbers

e.g.
$200049.60 as the starting balance for the 2 weeks
byweekly payments
4.75% interest
the bank shows accrued interest online, which I copied down a few of, unfortunately they do now show the history, just the current accrued interest.
e.g.
257.46
283.22
308.99
334.76

.. nice to see how your debt grows on a daily basis

anyways, that makes the daily interest around $25.75

my calculations of 200049.60*(0.0475/365) = $26.03
Close, but not the same.. any idea what the bank does to calculate the interest?.. I suppose I could call the bank, but chances are Murc is smarter than any telephone rep I may get

[Brian Ellis]

I assume that you are paying off some capital, as well as the interest, so that the interest will diminish as the year goes on. I think you may find they use a daily interest rate of 0.171% on the current outstanding capital (most banks in Europe work on a 360-day year for interest calculations, so that it can be used for calendar-monthly or annual rates). According to the type of contract, the actual calculations may be done daily, weekly, bi-monthly, monthly or annually: check the fine print!

[Tjalfe]

we pay $650/14 days, out of which ~$360 right now is interest.. the minimum payment the bank wanted was $622, so we have already knocked a few years off the mortgage.
I am here just calculating the interest in the 2 week period between a payment, which is where my math is failing me

[cjolley]

Amortization calculations are complicated.

Poke around in this site for info.

It's possible that calculations are done differently outside the US, but something like this should apply.

[Umfriend]

I get to 25.81, so it is closer

I guessed that the 4.75% was quoted as an effective annual rate. The actual rate of accrual is less as you pay interest more frequently and typically it is assumed this interest will be reinvested at the same rate. Assuming you _can_ reinvest at 4.75% APR (I think is the US term) you get:
I = (360/14)*((1+APR)^(1/(14/360))-1) = 4.64%
A = 200,049.60 x 4.64% / 360 = 25.81

Of course, it's always the details that is the devil; 360, 365 or 365Actual, how exactly do they decompound etc.

Ask your bank and be ready for shitloads of fun (if you're into that kind of thing).

Edit: Just to clarify how on earth 4.75% could be the same as 4.64%: If you take out a loan of $100 at 12% interest a year, how would you like to pay your interest?
(1) $12 at years'-end
(2) $1 each month.
Most people would prefer the former. So the next question is what rate of interest would you be willing to pay *if* you had pay monthly and had 12% annually as an alternative? Less than 12% obviously. The formula above is derived from a more commonly used formula (r = f x ((1+I)^(1/f))-1), where I is the quoted rate, r the actual rate of accrual and f the payment frequency. It is not a "correct" formula and indeed operators in the capital markets use a more profound approach to answer this question but for everyday use for normal people lik eus it suffices.