q23 in stella 2003

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wxyz

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as of jan 1, 20x1, an annuity offers $5,000 per year for seven years with the first day due Jan 1, 20x6. Ifthe annual interest rate is 11.5%, which is the present value of the annuity:
a. $13,453
b. $15.000
v. $23,185
d. 30.348
 
A).

N=7, I/Y = 11.5, Pmt = 5000 --> PV (at year 20x6) = 23,185

PV (at year 20x1) = 23,185 / (1.115^5) = 13,453
 
this is a problem of annuity due,
so use BGN mode ,
N=7, I/Y = 11.5, Pmt = 5000 --> PV (at year 20x6) = 25,851
PV (at year 20x1) = 25851 / (1.115^5) = 15,000

Answer is B
 
B) 15k

This is an annuity that pays at the beginning of the year so

PV (Jan 1 06) = N=6, I/Y = 11.5 PMT = 5K ==> 20.85147K + 5K = 25.85k
(Or do what FWVAGABOND did but set your calculator to BGN for the payment)

25.85k / 1.115^5 = 15k
 
Thanks, the answer is B (#22),
but Stella use the annuity (not annuity due, that's why I post the question) to solve it:

N=7, I/Y = 11.5, Pmt = 5000 --> PV (at year 20x6) = 23,185
PV (at year 20x1) = 23,185 / (1.115^4) = 15k

it's only difference from fwvag is 4 used instad of 5 (step 2).

The answre is the same as financegal and james.

but I still have question (annuity):
N=7, I/Y = 11.5, Pmt = 5000 --> PV (at year 20x6) = 25,851
why the PV at year20x6? not 20x8, I think 20x1+7year should be FV

If PV is 20x1 already, we don need step 2:
PV (at year 20x1) = 25851 / (1.115^5) = 15,000

I'm confused.
 
wxyz

Best way to deal with this type of question is just scribble out a time-line to keep it strait and visualize the payment pattern.

Two stage question

First you need the PV of 7 year annuity due starting 5 years from now that will pay $5,000/year. which will come to term at 1/1/2013

You have that with $25,185

Now you want to find the PV of $25,185 at time 1/1/2001. Keep your calculator set at BGN and just discount back 5 year @ 11.5% to get the value at 1/1/2001

Think of it another way, if the question asked how much do you need to deposit today if you can earn 11.5%/year and need $5,000/year for 7 years starting 5 years from today.
 
thanks.
I thought 7 years start from 20x1.
you guys are right.
 
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