How much interest will i get?

astonsmummy

I have searched everywhere to find out how to calculate AER, unfortunately, i am terrible with maths and have no clue, was wondering if anyone could tell me roughly how much interest i would make if i saved £140 per month for 12 months in the halifax 7% AER regular savings account?
or if not, how i could find out?
thnx x

Chrismaths

***Maths alert!!!!***
This is what's known as a the sum of geometric series.

First you need to work out the monthly rate of interest. An AER is what you get if you compound your interest over 1 year, so the month rate of interest is (1+7%)^(1/12). To do this in excel, =1.07^(1/12) = 1.005654145 = monthly rate

The value of £140 saved for 12 months at 7% AER is therefore 140*(1-monthly rate^12)/(1-monthly rate) = £1733.42.

So the interest is £1733.42-140*12 = £53.24

However if you are a basic rate tax payer, you'll pay 20% tax on the interest, So that works out at £1722.43, or £42.43 of interest

YorkshireBoy

astonsmummy wrote:

I have searched everywhere to find out how to calculate AER, unfortunately, i am terrible with maths and have no clue, was wondering if anyone could tell me roughly how much interest i would make if i saved £140 per month for 12 months in the halifax 7% AER regular savings account?
or if not, how i could find out?
thnx x

Roughly £47 after basic rate tax.

Total deposited = 12 x £140 = £1,680

Interest = (£1,680 / 2) x 0.07 x 0.8 = £47.04

Where...

(£1,680/2) = your average balance during the year*
0.07 is the 'per unit' interest (7%)
0.8 is the 'after 20% tax' adjustment

* I've sometimes seen this expressed as (£1,680 / 12 x 6.5) and one of the maths experts will be along shortly to explain why (but it's something to do with the timing of deposits)! This will have the result of increasing your interest to £50.96

astonsmummy

thnx for that guys xx

equitydealer

astonsmummy wrote:

I have searched everywhere to find out how to calculate AER, unfortunately, i am terrible with maths and have no clue, was wondering if anyone could tell me roughly how much interest i would make if i saved £140 per month for 12 months in the halifax 7% AER regular savings account?
or if not, how i could find out?
thnx x

->£65.08

https://secure.ingdirect.co.uk/calc/isa/isaNew.jsp

Just fill in your details and ING's calculator does it all for you.

astonsmummy

Thnx equity dealer xx

jonesMUFCforever

3 different answers from 3 different posters!!
So who's right then?
LOL

Chrismaths

me

The second answer uses simple interest rather than compound. A 7% AER paid monthly is no 7%/12, but 1.07^(1/12)-1. That's where the difference comes in.

The ING takes an initial plus 12 months (13 months of interest), so that's the difference there.

astonsmummy

well, they are all roughly around the same amount, that'll do for me! x

grumbler

ejones999 wrote:

3 different answers from 3 different posters!!
So who's right then?
LOL

The correct answer is £63.04 (£50.43 net)

equitydealer wrote:

->£65.08 ...
https://secure.ingdirect.co.uk/calc/isa/isaNew.jsp ... Just fill in your details and ING's calculator does it all for you.

This is an incorrect result. ING use Gross PA rate, while 7% is AER. ING quote their rate as 4.5%AER/4.41%Gross PA. To use this calculator you must transform 7%AER to
(1.07^(1/12)-1)*12=6.785% Gross PA. For 6.78% Gross PA result is £62.99 (£50.39 net)

YorkshireBoy wrote:

. I've sometimes seen this expressed as (£1,680 / 12 x 6.5) and one of the maths experts will be along shortly to explain why (but it's something to do with the timing of deposits)! This will have the result of increasing your interest to £50.96

Yes this formula takes into account the fact that the first and subsequent deposits are made actually at the start of the months (not calendar ones), but not in the middle of the months. Explanation can be found here: Regular Savings Accounts discussion . This formula gives good results, although it doesn't take compounding into account.

Chrismaths wrote:

***Maths alert!!!!***
This is what's known as a the sum of geometric series.

First you need to work out the monthly rate of interest. An AER is what you get if you compound your interest over 1 year, so the month rate of interest is (1+7%)^(1/12). To do this in excel, =1.07^(1/12) = 1.005654145 = monthly rate

The value of £140 saved for 12 months at 7% AER is therefore 140*(1-monthly rate^12)/(1-monthly rate) = £1733.42.

So the interest is £1733.42-140*12 = £53.24

Almost correct, but with a small mistake. This calculation is for 140+140*q+140*q^2+...+140*q^11 series (q=1.07^(1/12) = 1.005654145).
In fact this should be:
140*q+140*q^2+...+140*q^12=140*q*(1-q^n)/(1-q) that yelds £63.04 (£50.43 net) - the same as ING calculator when correct rate is used.
Also there is special financial function in Excel that can be used:
FV(q-1,12,140,0,1)+140*12=63.04

See also:
Compound Interest Calculation
compound interest-how do I work it out?

kenshaz

equitydealer wrote:

->£65.08

https://secure.ingdirect.co.uk/calc/isa/isaNew.jsp

Just fill in your details and ING's calculator does it all for you.

but do not save with them ,site good,service, good ,simple to open account,brilliant best online bank by far,but rate uncompetitive