AER / Gross help

MRLX69

I've been looking at this and got a bit confused:
http://www.kaupthingedge.co.uk/OurProducts/InterestRates.aspx

Which one is the best in terms of interest gained?... I'm a bit confused looking at the AER and gross... I know the difference and have read the article about the difference on this site, but I've been trying to work out how they got the gross from the AER... what's the mathematical relationship? - I'm guessing that the 1 year term is the best bang for buck but I just want to make sure before I lock up some money.

Thanks all

tomstickland

Depending on the payment frequency.

† AER stands for annual equivalent rate and illustrates the interest rate if it was paid and compounded once each year.
†† Gross is the annualised rate before deduction of tax at basic rate (currently 20%).

meester

AER is the same as gross if interest is paid annually.

If interest is paid monthly, you earn interest on the interest over the year.

KE pay monthly interest. It's very simple to calculate monthly interest if you have a gross figure, it's just gross /12.

Hence each month new balance = old balance * (1+(i/12))

Over a year, AER = (1 + i/n)^n - 1 (n will be either 12, for monthly, or 1, for annual)

I.e. AER = (1 + .0631/12)^12 - 1

= 6.5%

This bank wants to pay interest monthly, and have decided on a 6.5% headline rate, so they have in fact worked back from 6.5% to find the gross rate

AER can be less than gross where the rate includes a short-term bonus.

MRLX69

meester wrote: »

AER is the same as gross if interest is paid annually.

If interest is paid monthly, you earn interest on the interest over the year.

KE pay monthly interest. It's very simple to calculate monthly interest if you have a gross figure, it's just gross /12.

Hence each month new balance = old balance * (1+(i/12))

Over a year, AER = (1 + i/n)^n - 1 (n will be either 12, for monthly, or 1, for annual)

I.e. AER = (1 + .0631/12)^12 - 1

= 6.5%

This bank wants to pay interest monthly, and have decided on a 6.5% headline rate, so they have in fact worked back from 6.5% to find the gross rate

AER can be less than gross where the rate includes a short-term bonus.

Thanks! - I'll look more into it tomorrow, too sleepy at the moment. A final note (since I'm too sleepy to work it out) - it does seem like the best value is the 1 year term right?

Exo

This conversion site will work out the figures for you.
http://www.stoozing.com/mon2yr.htm

Assuming interest rates remain low, the fixed term rates of around 6.7% look quite good. Just ensure you do not require any of the money during the fixed term or you may get penalised, resulting in loss of interest payments.

MRLX69

Exo wrote: »

This conversion site will work out the figures for you.
http://www.stoozing.com/mon2yr.htm

Assuming interest rates remain low, the fixed term rates of around 6.7% look quite good. Just ensure you do not require any of the money during the fixed term or you may get penalised, resulting in loss of interest payments.

Ah, so you're saying that the 36month fixed term at 6.7% AER would give me more than the same sum of money invested in the 12month fixed term at 6.86% AER re-invested three years in a row??

MRLX69

meester wrote: »

AER is the same as gross if interest is paid annually.

If interest is paid monthly, you earn interest on the interest over the year.

KE pay monthly interest. It's very simple to calculate monthly interest if you have a gross figure, it's just gross /12.

Hence each month new balance = old balance * (1+(i/12))

Over a year, AER = (1 + i/n)^n - 1 (n will be either 12, for monthly, or 1, for annual)

I.e. AER = (1 + .0631/12)^12 - 1

= 6.5%

This bank wants to pay interest monthly, and have decided on a 6.5% headline rate, so they have in fact worked back from 6.5% to find the gross rate

AER can be less than gross where the rate includes a short-term bonus.

Grrr, I know you showed me how to work out the AER given Gross, but it won't work for the fixed term accounts.... I just can't seem to get the AER correct. I want to know how to work it out myself - just interested in this type of stuff that's all.... - so I can put it in a program or something later if I wanted to.

Exo

MRLX69 wrote: »

Ah, so you're saying that the 36month fixed term at 6.7% AER would give me more than the same sum of money invested in the 12month fixed term at 6.86% AER re-invested three years in a row??

Not at all.

Assuming from the examples you give are the same for each i.e. compounding monthly interest, then the rate of 6.86% AER will give more return on interest, assuming no days are lost when re-investing and the interest rate remains at 6.86% AER throughout the period.

Can you actually get a fixed term rate of 36 months at 6.7%? Most will give lower rates in the subsequent years.
Icesave give 6.7% for 12 months, 6.6% for 24 months and 6.5% for 36 months.

Not sure that I wish to have my money locked up for 3 years in this current climate.

tomstickland

AER is the useful figure. It's essentially how much you end up with after a year divided by what you started with.

For an account that pays interest n times per year:
AER%=100*((1+Gross%/(n*100))^n-1)


Looking at the three acccounts.
6 month option pays 6.69% gross. Put that into equation and you get: 6.8%.

12 month options pays 6.86% once per year, hence gross and AER are the same.

36 month option pays 7.16% after 3 years. So in this case n=1/3.
Hence the one off interest payment is 3*7.16%, which is 21.48%. The annualised rate that is the cube root of this (x^(1/3)) and comes out as 6.7%.

The account with the highest AER is the best option. Hence option 2.
If you used this 3 years in a row your total interest would be
1.0686^3 = 22% (gross equivalent 7.3%).
If you used the 36 month option your total interest would be
3*7.16 = 21.48%