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Amortization formula for daily interest

Hi All, I am trying to work out how much my monthly repayments should be on a mortgage where interest is accrued daily.

I have tried working out the effective annual rate and then using the widely available formula where monthly interest is assumed but the difference to monthly repayments is minimal and results in a fairly large positive figure come the end of the mortgage period.

For example, a mortgage of 300,000 at 6.99% over 30 years gives a repayment amount of 2133.47 assuming monthly interest. This will leave

1.07 left after 30 years (close enough to acceptable). However, when trying to work with a daily interest, my calculations give me a monthly repayment of 2137.72 and that leaves me a figure of 1639.17 at the end of 30 years. How can I get this to a more realistic figure?

What's more, if I use an more extreme interest rate e.g. 15%, assuming monthly interest I get a repayment value of 4058.87 with the balance at -1.16 at the end of the 30 years. No complaints there, but when trying to work this out for daily interest, I get a monthly repayment of 4082.24 but in 31-day months, the interest is >4100 meaning I am paying more in interest than my repayments - thanks to Feb each year, the mortgage eventually comes down to ~27000 at the end of 30 years.

For even more extreme interest rates e.g. 30% my calculations would determine I owe 3,325,918.5 by the end of the 30 years!! (At 30%, that would actually be quite accurate!!)

Can anyone provide any guidance on where I am going wrong? Thanks Ryan (the distressed!!)

Reply to
oneicanremember
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You will need to reveal your formula and explain how you arrived at that answer, because it is wrong. For 300k, 6.99%, and 30 years using the "crafty building society" method (i.e. interest charged on a yearly basis, with the monthly payments simply being saved up without earning interest prior to being applied at the end of the year), the annual payments would be 300k*0.0699/(1-1.0699^-30), i.e. 24151.64, and hence the monthly payments would be 2012.64. Using the "honest bank" method, you have to convert th 6.99%pa to 0.5825%pm and then the monthly payments are 300k*0.005825/(1-1.005825^-360) which is 1993.89.

By not being so silly. What do you mean by daily interest? It doesn't make sense to apply interest at other than the payment frequency. But even if you did, you'd exepct the payments to go down, not up, so you must have done something wrong. Show your workings.

Reply to
Ronald Raygun

Thanks for your time!

The formula used to calculate the effective monthly rate given the annual rate with daily interest was gained from someone on another thread. This being r = (1+(i/100)/365)^ (365/12)) - 1)

(where i is the yearly interest rate)

this is then plugged in to Repay = P * r / (1 - (1+r)^ -360)

This gives 1997.87 if interest is calculated daily (1993.89 when interest calculated monthly) - not sure what I did last night to get the figures I did but something clearly went wrong!

This issue of interest > repayments does still exist for higher rates though!

FYI For monthly interest, I do the straight forward calculation of yearly interest / 12

Thanks again for your time, any input is appreciated!

Reply to
oneicanremember

You really mean "where i is 100 times the yearly interest rate".

OK, this formula is theoretically correct where interest is *applied* daily, but no lender actually does that. When they say "interest is calculated daily" it *does not mean* that it is applied daily, it only means that account is taken of daily fluctuations of the account balance. The daily calculated interest is accumulated in a separate account which doesn't charge (or earn, as the case may be) interest, and the balance of this interest account is then transferred ("applied") to the main account at the end of each month. Hence the compounding you get is still monthly and not daily. Therefore the correct r to plug in to the repayment formula is still just a twelfth of the annual interest rate.

OK

Reply to
Ronald Raygun

Fantastic! That is what I was missing, I was compounding the interest!

Re-adjusting my interest to be no days * interest * balance gets me much nearer my expected values

I would disagree with a twelfth the annual rate as when interest is calculated daily, when payments are made has a vital impact.

Thank you very much for your help!

Reply to
oneicanremember

A twelfth of the annual rate is the right rate to use *on average*, especially when payment is "made" by the lender pulling in the dosh by direct debit on exactly the right day.

In practice, a lender may charge n/m instead of 1/12, where n is the number of days since the last monthly statement (if the statement date is constrained by having to avoid weekends and bank holidays) and m is the number of days in the current accounting year (365 or 366).

Reply to
Ronald Raygun

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