Annual Interest versus Monthly Interest?

Milarky

MJSW,

On reading the last post [pun!] I thought there might be an error in your use of figures - leading to rounding differences that could explain the small differences in the examples you gave. However, I confirm there is a difference even using the more 'accurate figures'

ING: 4.89 (Gross) 'AER'. Using 3.91 as the 'net' figure (at 20%) is not as accurate are 4.89*0.8 = 3.912. So assuming ING actually pays 1/12th of this per month it would be 3.912/12 = 0.326% [exactly!]

And 1.00326 ^ 12 = 3.9829%

and not 4.0000%, as would be the case with 'annual' interest.

I also picked up on the point, earlier, that if the balance is being reduced [eg 'mortgage' or 'debt'] rather than increased [eg 'savings'] the 'benefit' shifts from annual to monthly compounding of 'charges'. And this is exactly how most mortgages calculate interest, I assume?

BTW, have you noticed that with credit card interest rates [for example] '14.9' APR is quoted as 1.167% per month. When I do the calculation 1.01167 ^ 12, though, I get 14.9[387]%. Whereas 1.149^(1/12) = 1.164% per month. I assume that they move the actual rate they charge as close as they can to the mid point of the least significant figure [i.e to be 1.1494999..] take the twelfth power of this, and round down to the nearset 0.001% monthly interest? Thus, if any rate is quoted as '5.9' (say) it may be safest to assume that it is '5.949'

System

??? ??? ???

Joe_Bloggs

Thankyou MJSW and Milarky.
It is clear that you both care about the tiniest fraction of a penny and the MSE forum members are all the better for the display of practical financial calculations that relate to everyday situations.

Do you prefer to be paid interest monthy or annually.
Are there tactical aspects to monthly interest that overcome the strategic benefits of annual interest. All this given that interest rates go up and up and occasionally down, at different times according to individual savings institutions.
J_B.

patrickroc

sorry for an obvious question:

what would happen if i had a savings account paying annual interest and i wanted to switch mid-year to a new higher-paying account?

would i get the interest accrued thus far with my closing balance, or is it the deal with annual-payers that you are locked in for at least a year if you want to collect?

i'm with ING and i like getting the interest each month. i am free (and tempted) to switch to one of the new higher-paying savings accounts, but most of them pay annually...

lisyloo

You would get your accrued interest when you close the account.

You are not tied in jsut because of the way the interest is paid.

bridiej

Getting very confusing this post, but surely if:

I had £100 saved and got 5% per month, in the second month I would get 5% on the original £100 PLUS the first month's 5%? And it would carry on??

Whereas

If I had £100 saved and got 5% per year I would get simply the £100 plus 5%??

Is this right? In which case unless you get a preferential rate for having annual interest you'd be better off with monthly? ???

lisyloo

Is this right? In which case unless you get a preferential rate for having annual interest you'd be better off with monthly?

It depends.
You have to be very careful when looking at rates and take notice of the letter afterwards.

For example AER means Annual Equivalent Rate.
This means the compounding that you mention (getting interest on your interest) has already been taken into account.

Often the rates quoted include this (so a 5% AER would actually be slightly less per month).

You need to take care and be sure you understand what the rate represents.

lisyloo

As an example a 5% AER on an annual account means you get 5% at the end of the year.

But 5% AER on a monthly account mens you get something like 4.8%/12 per month and it gets made up to 5% by getting interest on your interest i.e. compound interest.

Paul_Herring

I messed about with Excel - this any use to anyone?

Gross figures for monthly are from ING.
Gross figures for yearly are the assumed AER for the monthly figures.
Amounts are rounded to the nearest penny every month (i.e. no fractional pennies are carried forward)


Gross 4.89% 5% 4.89% 5% 4.89% 5%
Tax rate 0% 0% 20% 20% 40% 40%
Monthly Yearly Monthly Yearly Monthly Yearly
Deposit £1,000.00 £1,000.00 £1,000.00 £1,000.00 £1,000.00 £1,000.00
Month 1 £1,004.08 £1,000.00 £1,003.26 £1,000.00 £1,002.45 £1,000.00
Month 2 £1,008.17 £1,000.00 £1,006.53 £1,000.00 £1,004.90 £1,000.00
Month 3 £1,012.28 £1,000.00 £1,009.81 £1,000.00 £1,007.36 £1,000.00
Month 4 £1,016.41 £1,000.00 £1,013.10 £1,000.00 £1,009.82 £1,000.00
Month 5 £1,020.55 £1,000.00 £1,016.40 £1,000.00 £1,012.29 £1,000.00
Month 6 £1,024.71 £1,000.00 £1,019.71 £1,000.00 £1,014.77 £1,000.00
Month 7 £1,028.89 £1,000.00 £1,023.03 £1,000.00 £1,017.25 £1,000.00
Month 8 £1,033.08 £1,000.00 £1,026.37 £1,000.00 £1,019.74 £1,000.00
Month 9 £1,037.29 £1,000.00 £1,029.72 £1,000.00 £1,022.23 £1,000.00
Month 10 £1,041.52 £1,000.00 £1,033.08 £1,000.00 £1,024.73 £1,000.00
Month 11 £1,045.76 £1,000.00 £1,036.45 £1,000.00 £1,027.24 £1,000.00
Month 12 £1,050.02 £1,050.00 £1,039.83 £1,040.00 £1,029.75 £1,030.00
====== ====== ====== ====== ====== ======
Net rate 5.00% 5.00% 3.98% 4.00% 2.98% 3.00%



Copy of spreadsheet available at http://members.aol.com/paulherring/monthly-yearly-interest.xls

Joe_Bloggs

@Paul Herring
Can you provide a few words that summarise and illustrate the fundamental underlying mathematics illustrated in your table. A conclusion would also be of use. References for the equations would complete the study.
J_B.
PS The taxman has his chunk every month in a monthly real world situation. In the annual case the taxman gets a one off payment. A minor factor in my view. Well done and thankyou.
J_B.