Question 1: An account with an initial amount B earns compound interest at an annual effective interest rate $i$. The interest in the third year is $426$ and the discount in the seventh year is $812$. Find $i$.
The work for question 1 is simple:
$$\dfrac{B(1+i)^7}{B(1+i)^3} = \dfrac{812}{426}$$
This leads you to $i = 17.5 \%$
Question 2: The amount of interest on X for two years is $320$. The amount of discount on X for one year is $148$. Find the annual effective interest rate $i$ and the value of X.
The work for question 2 is much more complex: it involves setting up $X(1+i)^2 - X = 320$ and $X - \dfrac{X}{1+i} = 148$, then solving for X and i, leading to $i = .053$ and $X = 2934.48$.
What is the difference in wording between these two questions? How would I know which to do on an exam?
I don't see a difference in the questions as well. But I start in a different way at the first question:
This gives me the equation $B(1+i)^3-B(1+i)^2=426$
Mathematically the term is $B(1+i)^7-B(1+i)^6=812$
Factoring out
\begin{align} & B(1+i)^2\cdot ((1+i)-1)=426 \\ & B(1+i)^6\cdot (1+i)-1)=812\\ & \\ &B(1+i)^2\cdot i=426 \\& B(1+i)^6\cdot i=812\\ & \\ & \textrm{Dividing one equation by the other } \\ & (1+i)^4=\frac{812}{426} \end{align}
So basically the set up for the first question is not different to the set up for the second question-beside the term "discount".