Ct1 Chapter 12

[Krati Gupta]

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..

 

[Michael Hosking]

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.

 

[SNEHAV]

Could you also please elaborate on the solution for Qn 12.12.
I am confused on how the equation was established.

 

[actuary111]

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

 

[John Lee]

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 \(1+j = \frac{1.07^5}{1.2}\)

 

[actuary111]

Great! Thank you!