Annuity cashflow rate?

How far out is this rate? An annuity will pay out $25000 in perpetuity. First payment out is 4 years from today Funds deposited into an account immediately to grow at a 4% semi annually compounded rate. How much money should the investor donate today to fund the project? A $528,150 B $549,487 C $574,253 D $618,812 Now first things first 4% semi compounding = 1.02^2 -1 = .0404 0r 4.04% As it is a perp $25000 / .0404 = $618,812 A good start lets not fall for the answer D trap , just yet! To PV the $618,812 future payment,I used 1.02^2x4 0r 1.02^8 = 1.171659 This gives $528,150 which i was quite happy with as Answer A But no the correct answer is in fact B $549,487…Please could somebody let me in on the secret of finding the rate. Thanks for any assistance,I will leave you in peace for a while from my questions, cheers!

6 periods, not 8. Draw a diagram.

Dreary, thankyou very much for your help…makes sense now…cheers!

I’m not clear on how perdition got 4.04% … I always thought semi-annual was just I/2 = 4/2 = 2% What am I missing?

Err…not sure how this is for 6 periods? Shouldnt it be 4 years and 8 periods? 1Yr 2Yr 3Yr 4Yr Today-----------1----------2---------3----------4 (payment 4 years from today) 2---------2-----------2---------2 I sometimes hate these TMVs!

the present value of an ANNUITY DUE ( 4 years from TODAY) is always n-1. in this case 4-1= 3 and you have semiannual pay therefore it is 6.

chad17 Wrote: ------------------------------------------------------- > I’m not clear on how perdition got 4.04% … I > always thought semi-annual was just I/2 = 4/2 = 2% > What am I missing? That was the part I thought I understood?! as i stated you half the 4% but pay the interest twice in the same year for semi annual. I thought it was only BEY where you effectively break the rules and half the yield for semi. I was obvioulsy confused over the 4 periods, but can see the 3 if you sit down and map it out, not saying I wouldn’t make a similar mistake again on such a problem rushing to complete it…Tks for you help all.

by using half the annual rate and doubling the periods, you are compounding the rate.

My bad, I see your point perdition.

The perpetual annuity is interesting in contrast to question 12 on page 211 of the CFAI text. They use the formula PV = A / (rs/m) where rs is the nominal yearly rate and m is the number of periods in the year. I believe its because in that CFAI question the payment is made quarterly (it’s a preferred stock dividend) whereas here, we only receive the payment once a year (although it is stated in terms of a semi-annual compound rate). Hence, the necessary EAR conversion. Is this correct? Thanks, Ali

may be a stupid question. …how do u know its an annuity due from the question? does “From today” mean its an annuity due? Thanks