How is daily interest calculated?

SouthLondonUser

Lotak wrote: »

I hadn't realised that they calculate interest based on the annual rate divided by 365 and they actually do calculate interest on a simple basis (i.e. the number of days x annual rate / 365).
I always assumed it was as it was with the CUMIPMT formula, i.e. compounded, and not on a simple rate.

No, you are wrong again. The CUMIPMT formula uses simple interest, not compounded interest. You can verify that very easily if you build an amortisation schedule in a spreadsheet, calculate the interest paid between two periods, then do the same calculation with CUMIPMT. Of course the formula requires the interest rate to be the same throughout the period.

Think of it this way: compounded interest means reinvesting the interest. You lend 100 at 10 for 1 year. After 1 year it becomes 110. If you reinvest the 110 at the same 10%, after another year you get 121, etc. On a mortgage there is nothing to compound - there is an outstanding balance, and you pay interest on that. "Compounding" might only come into play if the bank were to charge interest on unpaid interest - which is something some countries allow, while others explicitly prohibit.

Lotak wrote: »

I'm completely shocked about this. I actually thought I knew almost everything about mortgage calculations.

Were your calculations wrong? Or were they correct but you just hadn't understood how they worked?

I trust you will agree it is quite worrying that someone working for a mortgage lender does not understand how interest is calculated...

Lotak wrote: »

I think you were a bit heavy handed with your criticism though, but I actually learned something today so I should thank you.

You're welcome :cool:

SouthLondonUser

getmore4less wrote: »

You need to know the method of calculation of the daily rate from the flat rate.

My barclays mortgage is daily interest compounded monthly.

What do your mortgage terms say, exactly?
How much do you want to bet that Barclays is charging you simple, and not compounded, interest? :beer:

A mortgage loan charges simple interest, not compounded interest. Please, let's not confuse the readers of this forum with wrong information - especially you, who have almost 22k thanks!

Your terms probably say that the interest accrues daily but is payable once a month, or something to that effect.

Compounded interest means reinvesting the interest but, as I said in the other post, as long as there are no arrears, there is nothing to compound / reinvest.

For compounded interest,
the balance becomes:

balance * ( 1 + rate) ^ periods

so the formula for the interest is that above minus balance

For simple interest, the formula for the interest charged is simply: rate * periods * balance.

For example, if you have a balance of £100,000 and your interest rate is 3%, the first month you will pay £100,000 * 3%/12 = £250 of interest. The next month, your interest payment will be less, because you will have repaid some principal in the meanwhile.

To be precise, there may be slight differences, from bank to bank, in how interest is calculated. Some may charge the annual interest rate/12 every month, while others may count the actual number of days and divide by 365. However, it's still simple interest, not compounded.

For example, these are the mortgage terms for Santander :

16.5 - page 7:
Except where condition 16.7 applies or where a particular interest period is longer or
shorter than a month, we will work out the interest we charge each day on the basis
that the interest we charge in each interest period is one twelfth of the interest we
charge in the year.

Finally, and this is only academic, it can be easily proven that, if you compare simple vs compounded interest, they are the same after 1 year, simple is higher before 1 year, and compounded is higher after 1 year.

E.g. the interest on £100 at 10% after 1 month is 0.7974 compounded, and 0.8333 simple. The respective formulas are: 100 * 1.1 ^(1/12)-100 and 0.1*100/12

amnblog

Two theories, assuming you have an interest only deal

Theory one - Revert rate

You have it wrong. For example what was 4.74 with BM Solutions is now 5.09.

Theory two - Added fees

If you have added fees to the lending in the past they are often added on a repayment basis skewing the calculations.

getmore4less

SouthLondonUser wrote: »

What do your mortgage terms say, exactly?
How much do you want to bet that Barclays is charging you simple, and not compounded, interest? :beer:

They calculate daily based on the daily balance

They add the interest monthly(overnight at the end of the month)

If you don't pay it they charge interest on the interest.

That's daily interest monthly compounding.

SouthLondonUser

getmore4less wrote: »

That's daily interest monthly compounding.

Not quite. That's simple interest, calculated daily, and charged (i.e. payable by you, i.e. added to the balance, etc) monthly. There is no compounding as long as as there are no arrears.

Watch out with the use of the word "compounding" - it might be misinterpreted as meaning that the interest is compound interest; it is not, it is simple interest.

I don't really care what you want to call it - I just think that the readers of the forum should not be confused, and that it needs to be made clear it is simple, not compound, interest.

Just look up the definition on any dictionary.

https://www.merriam-webster.com/dictionary/compound
to compound: to pay (interest) on both the accrued interest and the principal

or

https://dictionary.cambridge.org/dictionary/english/compound
to compound: specialized / finance & economics / used to refer to a system of paying interest in which interest is paid both on the original amount of money invested (= given to companies hoping to get more back) or borrowed and on the interest that has collected over a period of time