SOA Practice problems #3 (Interest Theory)

On the practice problems for Interest Theory, I am getting a bit hung up on #3.



Here is the question:



"Eric deposits 100 into a savings account at time 0, which pays interest at an annual nominal rate of i, compounded semiannually



Mike deposits 200 into a different savings account at time 0, which pays simple interest at an annual rate of i.



Eric and Mike earn the same amount of interest during the last 6 months of the 8th year.



Calculate i."



So here is how I would go about it:



I would set up the amount of interest accumulated in the last half of the 8th year for Eric with this:



interest accumulated = 100*(1+i/2)^17 * (i/2)



And I would set up the amount of interest accumulated in the last half of the 8th year for Mike like this:



interest accumulated = 200(i/2)



Setting these equal to each other I arrive at:



100 * (1 + i/2)^17 + (i/2) = 200(i/2)



Simplifying this,



(1+i/2)^17 = 2 ...and then I would just solve for i (getting 8.323%)



But, this is wrong! The answer published by the SOA has:



100*(1+i/2)^15 * (i/2)= 200 (i/2)



Why would they raise this to the 15th power instead of the 17th power?



Thank you in advance!



Ok... and, in the answer, the initial explanation of the "interest earned" is as follows"

Quote:

Eric’s (compound) interest in the last 6 months of the 8th year is 100(1+i/2)^17 * i/2 Mike’s (simple) interest for the same period is 100(i/2)

Eric's makes sense to me here... but Mike's- not so much. Why would we multiply it by only 100, then use 200 in the equality to solve for i?



I am not trying to critique the answer's lack of clarity- it's more like, I'm not sure where I'm exactly going wrong- is it in the initial setup? I just didn't think I was messing up my timeline here

(like- 8.5 years = 17 periods) and it seems as though the initial setup verifies that.



So- I am ruling that out and thinking something else in my setup is wrong?!

SOA Practice problems #3 (Interest Theory)