Daily interest miscalculation?

[Deleted User] · 26 September 2007 at 8:58PM

Hi,

I embarked on a small mini-project recently that stemmed from a desire to repay our mortgage early, and calculate the term by which we'd need to reduce our mortgage (and, thereby, the monthly payments we'd need to make) in order to repay it in the timescale we have in mind.

I duly wrote a Perl script (for the non-technical, Perl is a programming language) that would calculate the outstanding balance on a daily basis - as our building society charges interest daily.

When we took out our mortgage (or rather, when we remortgaged), we were advised that the annual interest rate would be 4.95%, with interest calculated daily.

So I wrote my script to calculate daily interest based on a compound interest calculation from the annual interest (an annual interest rate of 4.95% amounts to a daily rate of 0.013237550135%), so that the cumulative daily interest on a £100,000 loan, with no repayments, would result in a balance of £104,950 at the end of one year.

What I quickly discovered was that the daily interest being applied did not tally with the daily interest being charged by my building society.

A little jiggery-pokery later, what I since discovered is that I am actually being charged a daily rate of 0.013561643836% - which would only be equivalent to an annual rate of 4.95% if the calculation were based on simple interest, not compound interest. In other words, they've simply divided their advertised rate of 4.95% by 365 and applied that figure daily.

What this means in reality is that an initial loan of £100,000, with interest calculated on my building society's basis, would result in a year-end balance not of £104,950, but around £105,742.

Is it just me, or does this seem - well - wrong?

danm · 26 September 2007 at 10:07PM

im not sure i get what you are saying.

By them not compounding the interest surely you are better off.

i.e, on day 1 they charge interest => 100,000*4.95%/365 = (lets call this i)
on day 2 do they do the same, or do they charge you interest on the 100,000 plus the previous days interest?

InMyDreams · 26 September 2007 at 10:13PM

But you wouldn't normally pay interest on the interest on a mortgage. It is calculated daily, but like with monthly paying savings accounts, it is only added on monthly. With a savings account, it's only once it's added onto your account that you start to earn interest on the interest (ie it's calculated daily but only compounded monthly). With a mortgage, you clear the interest each month before it's had a chance to do any compounding. As you clear the interest each month, by the end of the year you will have only paid your 4.95% because you haven't had to pay interest on the interest. Now if you *overpay* your mortgage (but continue with the regular mortgage payments at the same amount as before) then the interest you save would have a virtual compounding effect due to the ever increasing little bit of extra capital that you are paying off each month by keeping the regular payment the same. Not sure if that last bit makes any sense... I know what I mean, but I've enjoyed a glass of wine or two this evening.

Even those who go interest only, managing their own capital repayments via some other vehicle, would still be paying the mortgage interest off monthly. I assume. Wouldn't they?

CLAPTON · 26 September 2007 at 10:18PM

I dont know what an annual interest rate is...is it an APR or something else ?

InMyDreams · 26 September 2007 at 10:21PM

danm wrote: »

im not sure i get what you are saying.

By them not compounding the interest surely you are better off.

i.e, on day 1 they charge interest => 100,000*4.95%/365 = (lets call this i)
on day 2 do they do the same, or do they charge you interest on the 100,000 plus the previous days interest?

Well I bet they *would* compound it if you didn't pay it off each month! I think the OP is suggesting that if he doesn't pay a penny to his mortgage company, he would feel aggrieved that he ended up paying more than 4.95% of the original balance by the end of the year.

I think the issue is that he is trying to compare his mortgage rate with an AER rate used for savings account.

toonfish · 26 September 2007 at 10:28PM

I too can't see the relevance here - they charge you interest at the relevant rate on the outstanding balance daily - that's it!

[Deleted User] · 26 September 2007 at 10:29PM

InMyDreams wrote: »

But you wouldn't normally pay interest on the interest on a mortgage. It is calculated daily, but like with monthly paying savings accounts, it is only added on monthly. With a savings account, it's only once it's added onto your account that you start to earn interest on the interest (ie it's calculated daily but only compounded monthly). With a mortgage, you clear the interest each month before it's had a chance to do any compounding. As you clear the interest each month, by the end of the year you will have only paid your 4.95% because you haven't had to pay interest on the interest.

But wouldn't you still end up paying 11 months' interest on the first monthly interest charge, ten months on the second, and so forth...?

[Deleted User] · 26 September 2007 at 10:33PM

toonfish wrote: »

I too can't see the relevance here - they charge you interest at the relevant rate on the outstanding balance daily - that's it!

Thanks toonfish for responding. I'll try to put it more simply.

If I charge you an interest rate of 6% a year, that's not the same as charging you an interest rate of 0.5% a month - because you'd also pay 0.5% a month for eleven months on the first interest payment, 0.5% a month for ten months on the second payment, and so on. So the actual interest payments, taken over a period of a year, would work out to around 6.168%, not 6%.

[Deleted User] · 26 September 2007 at 10:34PM

danm wrote: »

im not sure i get what you are saying.

By them not compounding the interest surely you are better off.

i.e, on day 1 they charge interest => 100,000*4.95%/365 = (lets call this i)
on day 2 do they do the same, or do they charge you interest on the 100,000 plus the previous days interest?

That's what I am concerned about.

danm · 26 September 2007 at 10:37PM

Marvin_the_Martian wrote: »

Thanks toonfish for responding. I'll try to put it more simply.

If I charge you an interest rate of 6% a year, that's not the same as charging you an interest rate of 0.5% a month - because you'd also pay 0.5% a month for eleven months on the first interest payment, 0.5% a month for ten months on the second payment, and so on. So the actual interest payments, taken over a period of a year, would be around 6.168%, not 6%.

But your payments are due monhtly, so this would only be the case if you do not make the payments as they fall due

If the IR is 6%, this is 0.5% per month. On a mortgage balance of 100,000 this is £500. If at the end of month one i pay that £500, then no compounding of interest will take place. If you do not pay that interest then in month 2 i will owe £500 + (£500*0.5%).

You need to assume you are going to pay.

[Deleted User] · 26 September 2007 at 10:45PM

danm wrote: »

But your payments are due monhtly, so this would only be the case if you do not make the payments as they fall due

If the IR is 6%, this is 0.5% per month. On a mortgage balance of 100,000 this is £500. If at the end of month one i pay that £500, then no compounding of interest will take place. If you do not pay that interest then in month 2 i will owe £500 + (£500*0.5%).

You need to assume you are going to pay.

That strikes me as a rather artificial interpretation: by that token you might as well argue that if you overpay, the interest is really less than 6%!

Daily interest miscalculation?

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