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scottie_517
April 22nd 2008, 10:13 AM
Hi all : )

First post here - and I'm going to kick it off with a question that's killing me at the moment.

Question is as follows:
A&B plan to make a perpetual endowment to a cause. Said cause requires \$4700 p/a to operate. Endowment will be handed over in 8 years time from now, and \$4700 will be withdrawn on the first day. To fund the endowment A&B will make regular deposits every 6 months into an account, first deposit made today. Rate of interest = 4% p/a, compounded semi annually. They want you to advise them on the following:
(a) what will be the amount of the endowment to be handed over in 8 yrs time?
(b) how much must they deposit every 6 months to accumulate the req. amount?

This is how I've attacked the question - any input would be much appreciated.

calculated the effective annual rate using k = (1+0.04/2)^2 -1
to get 0.0404

To calculate the amount of the endowment to be handed over in 8 years, I used the perpetuity formula to calculate the principle (in present value terms) required to continue paying \$4700 P/A in interest into the future indefinitely - pvp = c/k = 4700/0.0404 = \$116,336.63

This gives us the present value of the endowment to be handed over in 8 years time – to calculate the figure as a future value (in 8 years time), I substituted this present value into formula FV = PV(1+k)^n
=116336.63(1+0.040)^16 (16 compunding periods due to semi annual compounding over 8 yrs)

Gives FV of \$122,829.31

I used the FV, and compounding function on my Casio FC-200V with inputs
Interest rate (I) = 4.04, Future final value (FV) = 122829.31, Number of compounding periods 8 years x 2 months (N) = 16, Payments per year (P/Y) = 2, Compounding periods per year (C/Y) = 2

SOLVE PMT = -6579.58 (deposit required every 6 months to accumulate the req'd amount)

Have I gone about this question in a totally crazy way or does it look right? Please, please, anyone HELP!

Thanks in advance,
Scott