How is daily interest calculated?

pc77

Could someone tell me how much interest I will earn if I pay 500 a month into a saver bond for 12 months at 5.00 Gross/AER if the interest is calculated daily please?

oldfella

£162.50 before tax - interest is always calculated daily

Calchas

According to "What's The Cost":

http://www.whatsthecost.com/default.aspx

£138.56.

This figure is exclusive of tax.

It may not be exact, but it is in the same ballpark!

Calchas

oldfella is probably right.

I may have used the calculator wrongly!

rb10

You'll get around £160-£165 interest in the above example.

Daily interest is calculated by taking the balance in the account at the end of each day, and multiplying it by one-365th of the annual rate. So if the annual rate is 5% (i.e. 0.05), each day you get (balance) * (0.05/365). They then make a note of all these daily figures, and add them all up to pay the interest.

For Regular Savings accounts, there's a simpler approximation to calculating interest. If you pay in the same amount each month, at roughly the same time of the month, you should get approx. 6.5 * (monthly credit) * interest rate (e.g. 0.05 for 5%).

agsnu

http://www.moneysavingexpert.com/savings/best-regular-savings-accounts#savingscalc says £161.29 (gross)

oldfella

it also depends on when you add the £500 each month

pc77

thanks for the help!

Robert_Sterling_3

rb10 wrote: »

You'll get around £160-£165 interest in the above example.

Daily interest is calculated by taking the balance in the account at the end of each day, and multiplying it by one-365th of the annual rate. So if the annual rate is 5% (i.e. 0.05), each day you get (balance) * (0.05/365). They then make a note of all these daily figures, and add them all up to pay the interest.

For Regular Savings accounts, there's a simpler approximation to calculating interest. If you pay in the same amount each month, at roughly the same time of the month, you should get approx. 6.5 * (monthly credit) * interest rate (e.g. 0.05 for 5%).

OK let us do a little sum.
Put £10,000 in the bank at 5%
Annual interest £500

Now let us look at the daily rate.

each day the interest is +5%/365 = 0.01369863 %
approx

If you do the sum on a spreadsheet you will find that the total amount after 365 day is £10,512.67
Whereas it should be £10,500

I have posted this several times on MSE

For the cognescenti this is what you should do

Let R be the daily Rate

Let r be the annual rate

Then R= [ 1+r ]^( +1/+365) -1

In the example above

R = [ 1+0.05 ]^(+1/+365) -1 Which is 0.0133681%

Thus we do not divide the annual interest rate by 365

we extract a 365th root

I will bore you no more with the sum.

........................................................................

The daily rate is for real.

Monthy rates are fictitious they are certainly not 1/12 th of the annual rate

because months have 28, 29, 30, 31.

.............................................................................................................

rb10

Sorry if I'm being a bit slow here, just a few questions ...

Robert_Sterling wrote: »

OK let us do a little sum.
Put £10,000 in the bank at 5%
Annual interest £500

Now let us look at the daily rate.

each day the interest is +5%/365 = 0.01369863 %
approx

If you do the sum on a spreadsheet you will find that the total amount after 365 day is £10,512.67
Whereas it should be £10,500

But taking 10000 * 0.01369863 = £1.369863 interest accrued each day.

Multiply this by 365 days in the year gives £499.999995, close enough to be correct (given rounding).

So the total amount surely does end up as £10,500, as expected.

I have posted this several times on MSE

For the cognescenti this is what you should do

Let R be the daily Rate

Let r be the annual rate

Then R= [ 1+r ]^( +1/+365) -1

In the example above

R = [ 1+0.05 ]^(+1/+365) -1 Which is 0.0133681%

Thus we do not divide the annual interest rate by 365

we extract a 365th root

I will bore you no more with the sum.

But taking 10000 * 0.0013368... = £1.336806171 interest accrued per day.

Multiplying this by £365 gives a total interest paid of £487.93 during the year.

The daily rate is for real.

Monthy rates are fictitious they are certainly not 1/12 th of the annual rate

because months have 28, 29, 30, 31.

.............................................................................................................

Agreed!

Stompa

rb10 wrote: »

But taking 10000 * 0.01369863 = £1.369863 interest accrued each day.

Multiply this by 365 days in the year gives £499.999995, close enough to be correct (given rounding).

So the total amount surely does end up as £10,500, as expected.

Well given that the 0.01369863% has been derived from 5%/365, it's hardly surprising that multiplying it by 365 gives precisely 5%!

How the calculation should be performed though depends not only on how often the interest is calculated, but also on how often it is compounded.