A niggling question about interest- monthly or annual?

FiscalFox

I have a question that has been bugging me (and may have even been answered before?). If you could help with it that would be great! Please assume you are talking to an financial novice with the mathematical skill of a lemon (nb: I actually scored a 'B' at GCSE, but really copied most of the work from my neighbour- a total whizzkid).

Anyway...

On a lot of bank accounts, bonds, etc., it seems you can have interest paid into your account either: a) annually, or b) monthly.

From my experience, the annual interest payments are just a little higher, and therefore i've always gone for them.

Recently, i've thought, "what if i got the (slightly lower) monthly interest payments, and had them repaid into the same account- Would the magic effects of continually compounding interest actually result in me making more cash over a yearly period?!!"


-I really can't get my head round whether it would or not! Or whether i am just asking silly questions.

Ideas anyone?

grumbler

FiscalFox wrote:

...Recently, i've thought, "what if i got the (slightly lower) monthly interest payments, and had them repaid into the same account- Would the magic effects of continually compounding interest actually result in me making more cash over a yearly period?!!" ...

Usually magic effect results in the same interest earned over a year, but not always.
Example:
Nationwide e-savings account 4.75% AER/gross p.a. paid yearly
ING (in 2005) 4.65% gross p.a. paid monthly 4.75% AER.

You can see - AER is the same. And the arithmetics behind this is as following:

(1+0.0465/12)^12-1=0.0475

However:
Cahoot:
4.25% gross p.a. paid yearly
4.15% gross p.a. paid montly

(1+0.0415/12)^12-1=0.0423 - not exactly 4.25%, although difference is very small. [AER here is different from gross p.a. with annual interest because of the bonus paid for the first 6 months].

General rule: compare AERs ...

YorkshireBoy

You compare accounts by checking their 'Annual Equivalent Rates' (AER's).

You are correct in that the 'gross pa' for a monthly paying account is usually lower than the annual paying account. However, once the monthly interest is compounded up for the year, it will invariably be the same value (ie AER) as a yearly option from the same provider.

EDIT: Less detail and still beaten by grumbler!

FiscalFox

Cheers guys, your explanations really helped. Grumbler; cheers for taking the time to go through the maths- it makes sense in my head now! Yorkshirelad- thanks for the clear summary!

Brilliant!

innovate

Probably another one for grumbler/YB: when would you opt for monthly, when for annual? If you need the monthly income?

jimclark1967

innovate wrote:

Probably another one for grumbler/YB: when would you opt for monthly, when for annual? If you need the monthly income?

You seem to have answered your own question

I tend to go for whichever option has the higher AER. If they're both the same then go for monthly. If annual has a higher AER and you still need the monthly income just withdraw the interest you would have been paid each month.

(Other advantages are that if you are a non taxpayer one year and a taxpayer the following year you get to keep the full amount on all monthly interest paid in the first tax year)

JC

tomstickland

There was a very long thread about this a month or so ago.
You have gross annual rate.
Monthly rate is 1/12th of this.
Compounding lifts the AER up above the gross annual rate.

Like this

You can see - AER is the same. And the arithmetics behind this is as following:

(1+0.0465/12)^12-1=0.0475

ie: 1+ 1/12th of the annual rate is the monthly multiplier, this happens 12 times, so power of twelve compounding.