Hi Sophie
The question is: 'Calculate the exact value of TAbar:70:<1> assuming the force of mortality is constant between consecutive integer ages.' That wording means that the answer needs to be exact with the exception of the constant force of mortality assumption only. The method you've used is another good way of approximating the answer, but it uses a different assumption that's not allowed given the question wording (the assumption that the death benefit payment is made in the middle of the year on average, if it's made) so it will not get many, if any, marks.
You may well know all this but the symbol given represents an expected present value ('EPV'). To get an EPV, we need to sum [(amount) x (discount factor) x (probability of payment happening)] over all possible payment times. An exact answer for this EPV requires an integral rather than a summation given the possible payment are continuous (as the bar over the 'A' means the payment could be made at any time in the year in question).
The wording about being able to assume a constant force of mortality means that a constant force of mortality (mu) can be calculated based on the relationship between 'p70' and 'mu70'. (p70 can be calculated based on q70, which can be looked up in the Tables.) This would give an 'average' mu for the year, which is a reasonable value to be used for mu for this question if we're assuming it's constant from age 70 to 71, as required.
An integral expression would then need to be set up and solved, using this constant mu figure.
I haven't double checked the d and L you looked up from the tables, but your approximation was almost correct (as an approximation), and would have got a lot of the marks if the question hadn't said 'exact' and 'assuming the force of mortality is constant ...' In the TA:70:<1> formula, you needed to calculate 'v' as 1.075^-1 rather than 1.075 but, other than that, the method you've used looks good for an approximate calculation (ignoring the fact that it doesn't conform to the question wording).
Hopefully this helps. All the best with your studies.
