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Dmitrii · Jun 28, 2009, 12:00 PM

Hi All,
I was wondering if someone could verify my solution to the following problem:
A 10 year annual annuity due with the first payment occurring at date t=7 has a current value of 75,000. If the discount rate is 10% per year, what is the annuity payment amount?

here is my solution:
PVA due=PVA*(1+r)
PVA=75000/1.1=68181.82
PVA at t=7: 68181.82*1.1^7=132867.08
PVA=C*((1-(1/1.1^10))/0.1)
C=132867.08/6.1446=21623.51

Thanks.

ArcSine · Jun 28, 2009, 12:56 PM

Your answer is right on the money (pun intended).

An equivalent path to the answer would reason that if it's val at t=0 is 75K, then at t=6 it's worth $75,000(1.1)^6$ .

And at t=6 it's an ordinary annuity, with the first CF occurring one year out. You could apply your ordinary annuity formula against the t=6 value to figure C, just like you did in your last two steps.

Cheers!

Dmitrii · Jun 28, 2009, 03:54 PM

Originally Posted by ArcSine

Your answer is right on the money (pun intended).

An equivalent path to the answer would reason that if it's val at t=0 is 75K, then at t=6 it's worth $75,000(1.1)^6$ .

And at t=6 it's an ordinary annuity, with the first CF occuring one year out. You could apply your ordinary annuity formula against the t=6 value to figure C, just like you did in your last two steps.

Cheers!

Thank you.