Example 12.11 on page 22 I am unable to understand its solution.. Please explain that how we hv got the equation of present value using annuities..
We start by pretending that the purchase was made one month later than it actually was. If this had been the case, the first dividend would have been in a year's time. So the first dividend term has v^1 in it. But the last dividend was 8 euros. The dividend paid today is 8x1.04, and the dividend in one year's time (which is the first dividend you will receive) is 8x1.04^2. Finally, we add an extra factor of v^{1/12} to allow for the fact that the purchase was made one month earlier.
Could you also please elaborate on the solution for Qn 12.12. I am confused on how the equation was established.
Example 12.12 increasing compound annuity I understand how the price equation is given in this example. But I don't understand how the j% is determined.. What is the logic behind forming the equation 1+j = 1.07^5/1.2 which is used to evaluate the 16 year annuity due? Anyone who understands and could shed some light on this? Thank you
Personally, I would have just used geometric series. However, the idea is that we set \(V = 1.2v^5\) this means that we now have: \(1 + V + V^2 + ... + V^{15}\) This is an annuity due for 15 years. Since \(V = \frac{1}{1+j} = 1.2v^5 = \frac{1.2}{1.07^5}\) hence \(1+j = \frac{1.07^5}{1.2}\)
