How is the interpolation done? I did it as (68-65/65-60)=(x-11.372/11.372-11.849) and getting a different answer than the solution given. Also since the annuity is payable monthly why is value 11/24 not subtracted?
There isn't any interpolation, so I'm afraid I don't understand your question. We write the reversionary annuity as a single life annuity to (60) minus a joint life annuity to (68) and (60). Then use the formula on Page 36 of the Tables for monthly annuities. The 11/24 terms cancel.
Ah, sorry, with you now. We are interpolating between the values of a(due)68:58 and a(due)68:63. 60 is 40% of the way between 58 and 63, so we apply a weight of 0.4 to a(due)68:63 and a weight of 0.6 to a(due)68:58.
Your terms in the denominator on the RHS are the wrong way round. Also, I don't follow your logic on the LHS. We're interpolating between ages 58 and 63. You do have the correct proportion of 3/5 though. You seem to be making it much harder than it really is. Interpolation is just about taking a weighted average of the two values that you are between. To work out the weights, just think about the percentage of the way you want to go between your first value and your second.
