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.

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!

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.