SAVINGS CALCS

scuba_scot

Hi all you MSE's, need some help with how interest is calculated on monthly saver accounts.

For example; if I invested £100.00/month in a savings account paying say 5.00% net monthly and re-invested, what would the balance be at the end of 12 months.
I know this must sound basic stuff to some of you, but if I can understand how companies work things out it should stand me in good stead for future saving.
Many thanks Scuba

Robert_Sterling_3

If you put £100 in a 5% account for 1 year you get £5 interest.  You may pay £0 or £1, or £2 tax on the interest.
Every thing else is pro rata to that.
They use a computer.

£100 per month for a year.
After 1 year you have  £1200 capital
But on average and not using a calculator and just
going for a "ball park figure" the amount in the
bank is £600.
So at the end of the year the total interest is in the region of £30 gross   After tax  £30 or £24  or £18.

Total after one year £1230 or £1224 or £1218.

Walletwatch

Hey Scuba

To add to the previous comment, the banks themselves more or less do it for you, by giving you two rates. The monthly interest that you earn can be calculated by using the gross rate, and then deducting tax. If the interest earned monthly is going to be reinvested, then the annual effective interest rate is what is represented by the AER quoted.

To illustrate, ING has a gross interest rate of 4.89% and an AER of 5%. This means that if you were to invest £100 on Jan 1, the interest for the month of Jan would be :

100 * 31 (no of days) * 4.89/(365*100) = 41.5p

Assuming that you do not withdraw this, you can calculate what you will make at the end of the year by using the AER as follows:

100*365*5/(365*100) = £5.

Hope that makes sense...

HTH

Doomcaster

http://www.fool.co.uk/savings/savings.htm

This may help, scroll down the page and click "Savings Calculator".

I use it all the time

lipidicman

To illustrate, ING has a gross interest rate of 4.89% and an AER of 5%. This means that if you were to invest £100 on Jan 1, the interest for the month of Jan would be :

100 * 31 (no of days) * 4.89/(365*100) = 41.5p

Assuming that you do not withdraw this, you can calculate what you will make at the end of the year by using the AER as follows:

100*365*5/(365*100) = £5.

Hope that makes sense...

HTH

No, no NO!

you cannot divide a yearly rate to get a daily rate, you cannot do it. Stop it, now!

Consider this: If you got 10 percent a day you would not have 100% interest on top after ten days(10*10). Rather, after ten days you would have multiplied by 1.10 ten times, ie
1.10^10=2.59 or 159%.

If you want a daily rate do 1.05^(1/365) for 5%
this is 1.0001336 or a daily rate of 0.01336%
whereas you make it 5/365 = 0.01369%

a 0.00033% difference might not seem much, but it adds up, as the ten percent example above shows (where you have 159% rather than 100%) because you must apply this daily rate to the power of 365 to get the yearly rate , and that is where the 0.01336 and 0.01369 will make a big difference.

Using division misses out the whole benefit of compound interest. And this is how the banks do it

Walletwatch

No, no NO!

you cannot divide a yearly rate to get a daily rate, you cannot do it. Stop it, now!

Consider this:  If you got 10 percent a day you would not have 100% interest on top after ten days(10*10).  Rather,  after ten days you would have multiplied by 1.10 ten times, ie
1.10^10=2.59 or 159%.

If you want a daily rate do 1.05^(1/365) for 5%
this is 1.0001336 or a daily rate of 0.01336%
whereas you make it 5/365 = 0.01369%

a 0.00033% difference might not seem much, but it adds up, as the ten percent example above shows (where you have 159% rather than 100%) because you must apply this daily rate to the power of 365 to get the yearly rate , and that is where the 0.01336 and 0.01369 will make a big difference.

Using division misses out the whole benefit of compound interest.  And this is how the banks do it

Don't quite see what you are driving at, mate !!!

What I've said is perfectly valid, would like to know the specific calculation which you think is wrong... £100 in an ING account does earn you 41.5p in a month, and if you do not withdraw the interest, then in a whole year, you can apply the AER to say how many pounds you will earn in a year for a deposited amount of £100 (in this case, ING having an AER of 5% would give you £5 at the end of the year for a £100 deposit with all the interest reinvested)

Should you wish to get more technical, the 5% is calculated as follows:

AER = ((1+((4.89/100)/12)¹²) - 1

= (1.004075¹²) - 1

= 1.050011 - 1

= 0.05 or 5%

Having been a banker myself, and been into Corporate Business development, I wouldn't dream of 10% for ten days meaning 100% as you say...

Come to think of it, I wouldn't really mind such an account, so far as I get the right end of the stick... i.e. I am a saver and not a borrower

scuba_scot

Thanks for all the replies folks they have enlightened a great deal as to how the financial-institutes do there calculations.
I would like to have 3 possible options set up for a percentage of my income each month.

1- A good savings account where interest is re-invested every month for the forseeable future.
2- A small risk option possibly a bond or similar where i can put a small portion of my income.
3- Lastly an investment vehicle with more risk where I can invest some of the interest from option 2.

Any of your thoughts on of these points would be gladly received.
Yours Scuba

lipidicman

Walletwatch

I didnt mean to upset you and I guess I was a little unfair to quote your post. I was being picky about all the posts in general and was trying to help the original poster. I did fail to notice that you were using the gross rate and the AER.

One thing I did find strange was this

100*365*5/(365*100) = £5.

where the 365's and the 10's cancel and that is why it will work. It wont work for any other number of days, will it?

For anyone who wants to clarify matters if we have confused them, try:
http://www.bba.org.uk/content/1/c4/19/28/aer-3.pdf
which explains why the AER and the gross rate are different (the AER is determined by the gross rate and the frequency of payments)

Again my apologies to Walletwatch

Walletwatch

lipidicman

Not an issue, was just taken aback, and well, you did make me re-read my post to ensure I hadn't made a typo... ;D

As for your question, yes it would apply only for perfect years, but then, that is what I mean when I say in my post ... 'what you make at the end of the year....'

Cheers