Help on Nominal and effective rate question

If an amount £10,000 is invested now and accumulated for two years. The interest rate is 8% per annum payable half yearly. Calculate:

a) The effective annual rate of interest earned;

why isit (1+0.08/2)^4=(1+i)^2

Why for the effective rate is it (1+i)^2.. and not (1+i)??

I would appreciate it if someone could please help me on this bit.

Thanks in advance!

 

We have the following fundamental relationship:
(1+i^(p)/p)^p = (1+i)

where i^(p) = nominal interest rate payable pthly
i = annual effective interest rate

Based on the info given in the question we therefore have:
(1+0.08/2)^2 = 1.08. This is the same as saying (1+0.08/2)^4 = 1.08^2.

Over two years, there are 4 six monthly periods. Similarly there are 2 annual periods. Therefore, these two facts are used when setting up the fundamental equation.

 

Hi All,

In relation to the above, I don't see the how \((1+0.08/2)^2 = 1.08\) is derived. The 8%p.a. convertible half yearly is considered to be the nominal interest rate, correct?

 

Nor do I. I think it is an error.

An interest rate of 8% pa payable (ie convertible) half-yearly is a nominal interest rate, so the accumulation factor for 1 year is:

(1 + 0.08/2)^2 = 1.04^2 = 1 + i (where i is the annual effective rate)

and the accumulation factor for 2 years is:

(1 + 0.08/2)^4 = 1.04^4 = (1 + i)^2