Can someone please explain the difference between %AER and Gross Interest?

Question

Can someone please explain the difference between %AER and Gross Interest?
Ok, i know the Net Interest is after tax, but what is the Difference between 5.77% AER and 5.62% Gross?

Answer 1

AER is calculated as if compounded annually.

If (gross) interest is applied monthly, then the AER will be higher (because with the gross interest you are getting 'Interest on the Interest').

AER = (1+i/n)^n - 1

where i is the 'nominal' rate, and n the number of compounding periods per year (for example, n = 12 for monthly compounding):

For example, a nominal interest rate of 6% compounded monthly is equivalent to an AER of 6.17% as follows :-

6% monthly is credited as 6%/12 = 0.5% every month.

At the end of the first month you have an extra 0.5% in your account.

When the second months 0.5% interest is applied, you get an extra 0.5% 'on top of' the first 0.5% i.e. an extra 0.5% of 0.5% = .0025%. This is added to you account (so you have 2 months interest i.e. 1%, PLUS the extra .0025%)

Month 3 you get 0.5% PLUS an extra 0.5% of 1.0025% .. and so on.

After 12 such months, the initial capital is increased by ≈ 6.17%

(the extra 0.17% is the result of getting 11 months worth of 'interest on the interest')