Hi! I've been working on this problem and I finally figured it out! Bear with me b/c I do not know how to do "math symbols" on the computer.
The accumulated value in option 1 = 10,000 * (1+i)^24
The accumulated value in option 2 = X * s(24).05 --> Here the ( ) is representing the annuity symbol
X is each payment, which is deposited into a fund earning 5% over the 24 years
We need to figure out X. Let's use the information about our annuity-immediate.
10,000 = X * a(24).10
Now we can solve for X, which we find to equal 1112.997764
Now we set our two accumulated value functions equal to each other.
X * s(24).05 = 10,000 * (1+i)^24
(1112.997764) * s(24).05 = 10,000 * (1+i)^24
Just solve for i and you get .068939.