level annuities

what is the difference between immediate annuity, payments made in advance & continuously payable annuities????

 

They are not directly related that its too tough to get difference between them.

May this work,
1) immediate vs differed annuity:-when the first payment has made in the first time period (whether in advance or in arrears) is called Immediate annuity otherwise it will called as deferred annuity.
2)payment made in advance vs payment made in arrears:- if each and every payments made in start of the each period is called as payment made in advance and if each & every payments is made at the end of the each period is called as payment made in arrears.
3)continuously payable annuity vs discretely payable annuity:- they are if payments made continuously or discreetly respectively.

 

In a problem if they ask to find out the present value of a series of payments ,how we will come to know to use (A.N. , A due N , A bar N) which formula (in the bracket)?
Can u differentiate those 3 formulas?

 

Let the time period of payments be 1st Jan, 2015 to 31st Dec, 2010
Let you are at 1st Jan, 2015
If the payment starts on 1st Jan,2015 annually then you use adue_n
If the payment starts on 31st Dec,2015 annually then you use a_n
If the payment starts on 1st Jan,2015 & payable continuously(you can say daily) then you use abar_n.
And important thing, My example was for Immediate Payment.
Now for deferred payments apply same logic for what to find a_n or adue_n or abar_n , but payments deffered for few(let m) years(for this you multiply by v^m)

 

thank you I understood what u said
still I am having some doubts in level annuities
in pg-15 of ch-6, there is an example;in the 3rd line of the solution he took 'v' but why should we take 'v'

 

Because \( 1200*\require{enclose}\ddot{a}_{\enclose{actuarial}{3}}^{(12)} \) is present value at 1st Jan, 2015 but you need at a year before.

If you think to apply \( 1200*\require{enclose}a_{\enclose{actuarial}{3}}^{(12)} \) , then its wrong. Because, it means present value of payments for 31/3/14 ,30/6/14 ,30/9/14 so on.

 

thank u
in question 6.8, how did we get 0.66227% in the solution

 

As 8% rate is convertible quarterly,
Annual effective rate is (1+.08/4)^4 - 1=.08243216
Then monthly rate is 1.08243216^{1/12} -1 = .0066227 i.e. .66227%

 

thank u so much