CT1- Level annuity, Non-integer value of n

[Bharti Singla]

Please anyone explain the definition highlighted in the below attached pic. The LHS is the PV of annuity of 1 pa payable half-yearly for 23.75 years.
But I didn't get the term 1/4v^23.75 on RHS.
Since the payments are half-yearly, the last half-yearly payment should be made at the end of 23.5th year and there should be no payment on time 23.75. Then why they have included this term in RHS?
How 1/4 can be made at time 23.75 even if the payments are half-yearly?

Please rply asap.
Thanks

 

[Pede]

That's the point. They're saying that if you're referring to an annuity with a strange length (eg 23.75, even when payments are only half-yearly), then some practitioners would say that the annuity of the strange length is just the normal one plus an extra bit at the end.

It's like saying I buy a box of chocolates at the start of every month. But if somebody told me to buy chocolates for 3.5 months, then some people might take that to mean that I buy 3 boxes, then half a box two weeks later. I don't really, but that's how some might interpret it.

 

[Bharti Singla]

Ohkay, its different ways of interpreting. Got it, Thanks