PV annuity

[Hokkaido]

Jack is to receive six quartely payments of $1,000 under his uncle's will. the first of the payments will occur two years from now when he turns eighteen. how much would yoube prepared to pay Jack now for his endowment if the interest rate is J4=20%

i used PV=C*PVIFA(n,r) and then PV=Fv(1+r)^-n

but my answer was wrong and the correct answer was $1,688.

Can you help me?

[bednobs]

how can an answer be wrong if it's asking you for your opinion on how much YOU'D be PREPARED to pay.
For myself, it would be about $500

[dzug2]

I'd pay him nothing now - let him wait.

[factor-fiction]

Well I did a quick calculation on the back of an envelope and got an answer of $1618 so the correct answer seems a little high. What answer did you get?
The quarterly payments are $166.67. The first payment earns 2 years' interest at 20% pa so is worth $240.
The next payment of $166.67 earns 2.25 years' interest so is worth just over $251.
And so on

[factor-fiction]

Maybe I misinterpreted this completely as I assumed you meant you received a real interest rate of 20% on the money while you were holding it prior to paying out a total of $1000 in the form of six small payments.

But now i'm wondering whether you meant six quarterly payments of $1000 dollars each

[squarebear]

You would pay him $1,688 for six lots of $1,000?! I hope he tells you to pee off.

[dr b]

I don't understand "if the interest rate is J4=20%", but assuming the annual rate is 20%, that's 5%/quarter, so the PV is:

1000/(1.05)^8 + ... + 1000/(1.05)^13 = $3607

since you will receive 1000 at the end of quarters 8, 9, 10, ... 13.

If the quarterly rate were really 20%, the PV = 928. In order for the PV to be 1688 as stated, the quarterly rate would have to be 13.1%, so that answer seems incorrect.

[factor-fiction]

... except an annual rate of 20% pa is not quite the same as a compounded rate of 5% per quarter- the quarterly rate would be nearer 4.7%
(1.047^4=1.20)

[dr b]

But by convention you use annual percentage rates, not effective annual rates, so you would take 20%/4.