The question reads:
Find the nominal rate per annum convertible quarterly that makes an interest payment of £150 on an initial capital of £1,000, at the end of 2 years.
Could somebody clarify for me whether this 'interest payment' means the accumulated value of the 8 interest payments made over the two years, or otherwise?
I know that this question is very basic but I really need to get to grips with this terminology and also how to approach the question in general.
When they say "nominal annual rate compounded quarterly," they mean that the rate of interest is stated as $i$ per year, but it really means ${i\over4}$ per quarter. This gives an effective annual rate greater than $i$, since $$\left(1+{i\over4}\right)^4>1+i$$
In this case, we have $$1000\left(1+{i\over4}\right)^8=1150$$ and you just have to solve for $i$.
If you want to check your work, I get $7.0495\%$
In actuarial literature at least, $i$ would be written as $i^{(4)}$ to indicate a nominal annual rate compounded quarterly, and $i$ reserved for the effective annual rate, so we'd have formula $$i=\left(1+{i\over4}\right)^4-1$$