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jackel4849 · Oct 17, 2009, 06:14 PM

A 10-year annual annuity due with the first payment occurring at t=7 has a present value of $50,000 today. If the discount rate is 13% per year, what is the annuity amount?

morgaine300 · Oct 17, 2009, 07:31 PM

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https://www.askmehelpdesk.com/financ...nt-407093.html

jackel4849 · Oct 18, 2009, 10:21 AM

This is what I have done so far.
PVA=50000/1.13=44247.79
44247.79(1.13)^7=104097.59
PVA at t=7: ((1-(1/1.13^10)/.13)xC=5.43xC
C=104097.59/5.43=$19170.83 which is the annuity payment amnt

I need to know the annuity due, and don't know how to get there from the annuity payments.

ArcSine · Oct 18, 2009, 02:45 PM

If its value is 50K today, at a 13% discount rate, then it has a value of...

$50,000 \ \times \ (1.13)^6 \ = \ 104,098$ one year before the first of the ten payments, or equivalently, a value of...

$50,000 \ \times \ (1.13)^7 \ = \ 117,630$ on the date of the first payment.

You can find the annual payment amount either by using the 104,098 in the "present value of an ordinary annuity" formula, or by using the 117,630 in the "present value of an annuity due formula".

Note that in your work, by discounting the 50K back one period, and then compounding it forward for 7 seven periods, you've arrived at the same 104,098 as I have above, from just taking the 50K forward for 6 periods. You then determined the annual payment amount correctly, using the PV-of-an-ordinary-annuity formula.

Allowing for a little rounding, you've come very close to the correct answer. Where are you thinking that you haven't completed the problem?