I've got this problem which I'm sure I'm doing right, but it's not working. I'm hoping that if I explain what I'm trying to do on here someone could point out to me what's wrong, or maybe I'll discover my error while writing.

You are given Force_of_Interest(t) = 2/(t-1) for 2<t<10
For any one year interval between n and n+1, with 2<n<9, calculate the equivalent d(2).
Answer: 2/n
So, I'm gonna go about this by using the force of interest to discover the interest rate for a specific year. I know this won't give me the expression I need, but I can do the following conversion and check it with the different given expressions:

Force of Interest --> Interest --> Nominal Interest --> Nominal Discount Rate.

In fact, I am able to get Interest as a function of N identical to what the solution I have on hand shows, so my error is somewhere after this following expression of i:

i+1 = a(n+1) / a(n)
i = (n/(n-1))^2 - 1

Now, I'm going to substitute n in to this equation and follow the above implications until I get a number which should match one of the multiple choice answers. I'll use n=4, the interest rate during the 5th year (though that's irrelevant, right?) My error should be somewhere in here but I can't see what it is and it's driving me crazy.

i = (4/(4-1))^2 - 1
i = 0.7777777777
i(2) = 0.774905112
d(2) = 0.774905112/(1+0.774905112)
d(2) = 0.4365896

Though, this isn't any of the multiple choice answers. Substituting in 4 to the correct answer gives 2/4 = 0.5. Shouldn't it be the same as my d(2)?