In solution the amount who's present value is to be calculated is 1200. Why so? Why not 400 for first 4 months n same for next 4 months, because the question says, " 5 year annuity consisting of payments of 100, starting on Jan 2005 and payable on the first day of each month with an R in its name."
Apologies that this slipped through our net. If you don't get a reply then do email the tutor currently responsible for that forum. When you use annuities the three numbers (X, n and p) need to be consistent: \(\require{enclose}{}Xa_{\enclose{actuarial}{n}}^{(p)}\) Since we're working in years n = 4/12 of a year, p = 12 payments a year and X = £1,200 a year. Since the annuity only runs for 4/12 of a year we will only get the £400.
your formula implies 800 pa paid monthly in advance, ie 800/12 every month. We've got 100 each month with an R in it. Your might be a reasonable approximation but not an accurate formula.
Sorry, I don't think you can easily. I'd start again valuing the payments in Jan-Apr and then Sept-Dec as they do in the solution. the solution is pretty comprehensive and so I can't add much to that.
