# 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.