Confused about daily interest and compound interest

flaneurs_lobster

reg091 said:

Forget about the interest rate, is my assumption that the only account that pays compounded interest one that pays daily?

Doesn't really matter what method of compounding (daily, weekly, monthly or even annually) is used as long as the rate quoted is the Annual Equivalent Rate (AER) which tells you what your deposit will earn in interest after a year.

Important bit there is Equivalent, this means you can compare the earnings of two or more accounts having different compounding methods.

saajan_12

reg091 said:

Researching savings accounts and it seemed to me that by far the best option is interest paid daily  as it would compound. This can't be true or else why would anyone take interest paid monthly or yearly?

My understanding of an interest paid daily account is that if you start off with £100 and the interest rate is 5% the next day you have £105. The next day you have £110.25 etc.

If you opt for interest paid yearly then I understand it calculates the interest at the close of business every day of the year and adds those numbers together. So, there is no compounding.

I must be wrong! Everyone would have interest paid daily accounts and monthly/yearly wouldn't exist!

Can someone enlighten me please?

You need to be clear which interest rate you're talking about, regardless of how the interest is paid. The rate is almost always quoted as an annual % and either as a gross % or an AER %. The AER is just the equivalent rate taking into account the compounding over the course of a year. 

Eg 6% p.a. gross interest paid monthly with a £100 deposit has a 6.17% AER rate
Month 1: 100 x 6% / 12 = 0.50 interest -> balance £100.50
Month 2: 100.50 x 6% / 12 = 0.5025 interest -> balance £101.0025
...
Month 12: 105.63 x 6% / 12 = 0.5282 interest -> balance £106.16778 
Over the year, you earned £6.17 interest, with the extra 17p coming from compounding.
AER rate = £6.17 / £100 = 6.17% vs a gross interest rate of 6%. 

A 6% p.a. gross interest paid annually would earn £6. 
A 6.17% p.a. AER interest paid annually would earn £6.17. 

So basically if you compare AER interest rates, then whatever the frequency of payment, the compounding is already accounted for. 
Same effect for a daily paid rate, but the difference between the gross rate and the AER rate is higher. 

wmb194

Hoenir said:

Interest isn't added daily to the account. Interest is calculated daily. What's key is how often it is paid to the account holder.

The OP might have Trading212's GIAs and S&S Isas in mind as they credit interest daily.

ColdIron

reg091 said:

ColdIron said:

reg091 said:

My understanding of an interest paid daily account is that if you start off with £100 and the interest rate is 5% the next day you have £105. The next day you have £110.25 etc.

£5 a day, if only

You need to read and understand this

https://www.moneysavingexpert.com/banking/interest-rates/#save

Thanks. I do understand that but what about compounding?

Did you skip the section devoted to compounding in the link?

https://www.moneysavingexpert.com/banking/interest-rates/#compound

reg091

ColdIron said:

reg091 said:

ColdIron said:

reg091 said:

My understanding of an interest paid daily account is that if you start off with £100 and the interest rate is 5% the next day you have £105. The next day you have £110.25 etc.

£5 a day, if only

You need to read and understand this

https://www.moneysavingexpert.com/banking/interest-rates/#save

Thanks. I do understand that but what about compounding?

Did you skip the section devoted to compounding in the link?

https://www.moneysavingexpert.com/banking/interest-rates/#compound

ColdIron said:

reg091 said:

ColdIron said:

reg091 said:

My understanding of an interest paid daily account is that if you start off with £100 and the interest rate is 5% the next day you have £105. The next day you have £110.25 etc.

£5 a day, if only

You need to read and understand this

https://www.moneysavingexpert.com/banking/interest-rates/#save

Thanks. I do understand that but what about compounding?

Did you skip the section devoted to compounding in the link?

https://www.moneysavingexpert.com/banking/interest-rates/#compound

No, and that clearly explains the principle of compounding. But the example they use is for interest paid annually. If interest is paid daily (i.e. added to the balance of the account) then after one year you must have more than if paid once. I get that the daily interest will not be 10%.

eskbanker

reg091 said:

Forget about the interest rate, is my assumption that the only account that pays compounded interest one that pays daily?

No, the vast majority of accounts (except those that insist on interest being paid away) will compound interest, whether credited daily, weekly, monthly or annually, but the key message is that this isn't some money-making wheeze, as the interest rate paid will be calibrated according to the frequency.  In other words, the gross rate paid will be lower the more frequently it's paid, and, as above, the basis on which to compare is the AER, which factors compounding into its derivation in order to allow a standardised like-for-like comparison of the actual annual return.

reg091

eskbanker said:

reg091 said:

Forget about the interest rate, is my assumption that the only account that pays compounded interest one that pays daily?

No, the vast majority of accounts (except those that insist on interest being paid away) will compound interest, whether credited daily, weekly, monthly or annually, but the key message is that this isn't some money-making wheeze, as the interest rate paid will be calibrated according to the frequency.  In other words, the gross rate paid will be lower the more frequently it's paid, and, as above, the basis on which to compare is the AER, which factors compounding into its derivation in order to allow a standardised like-for-like comparison of the actual annual return.

Brilliant, thanks! So, if you had £1000 in each of three accounts, each with the same AER, and one crediting interest daily, one monthly and one annually, you would make the same exact amount of interest from each after 12 Months?

eskbanker

reg091 said:

eskbanker said:

reg091 said:

Forget about the interest rate, is my assumption that the only account that pays compounded interest one that pays daily?

No, the vast majority of accounts (except those that insist on interest being paid away) will compound interest, whether credited daily, weekly, monthly or annually, but the key message is that this isn't some money-making wheeze, as the interest rate paid will be calibrated according to the frequency.  In other words, the gross rate paid will be lower the more frequently it's paid, and, as above, the basis on which to compare is the AER, which factors compounding into its derivation in order to allow a standardised like-for-like comparison of the actual annual return.

Brilliant, thanks! So, if you had £1000 in each of three accounts, each with the same AER, and one crediting interest daily, one monthly and one annually, you would make the same exact amount of interest from each after 12 Months?

Yes, that's right, although strictly speaking there may be very minor rounding variances.

surreysaver

reg091 said:

eskbanker said:

reg091 said:

Forget about the interest rate, is my assumption that the only account that pays compounded interest one that pays daily?

No, the vast majority of accounts (except those that insist on interest being paid away) will compound interest, whether credited daily, weekly, monthly or annually, but the key message is that this isn't some money-making wheeze, as the interest rate paid will be calibrated according to the frequency.  In other words, the gross rate paid will be lower the more frequently it's paid, and, as above, the basis on which to compare is the AER, which factors compounding into its derivation in order to allow a standardised like-for-like comparison of the actual annual return.

Brilliant, thanks! So, if you had £1000 in each of three accounts, each with the same AER, and one crediting interest daily, one monthly and one annually, you would make the same exact amount of interest from each after 12 Months?

Unless you withdraw money. It may also affect how much tax you pay if some interest is credited one tax year and the rest the next.
If you withdraw money before interest is added, you may be better off with an account paying interest less frequently, as that will have a higher gross rate, even if the AER is the same.

ChesterDog

reg091 said:

ColdIron said:

reg091 said:

My understanding of an interest paid daily account is that if you start off with £100 and the interest rate is 5% the next day you have £105. The next day you have £110.25 etc.

£5 a day, if only

You need to read and understand this

https://www.moneysavingexpert.com/banking/interest-rates/#save

Thanks. I do understand that but what about compounding? Surely if the interest is added to your balance daily then you would get more than if it just added once at the end of the year? I understand that a quoted interest rate is an annual amount (AER) so in the example given of £1000 at 1% doesn't mean you get 1% per day, you get a fraction of that. But the principle of compounding with daily paid interest surely means you will get more than interest paid at year end.

When accounts allow options on how often the interest is paid, the interest rates will differ slightly between the different options, so as to result in the same AER.

For example, the rate for annual interest will be greater than that for monthly interest, so that the compounding effect of the latter is negated.