View Full Version : need help for sinking fund problem

Jon Ho

April 27th 2006, 01:18 AM

Question:

ACG inc has purchased a new machine at a cost of 255,000. the machine is expected to have a useful life of about 10 years and no salvage value. ACG is interest in establishing a "sinking fund" for the purchase of a new machine in 10 years. Research indicates than on an avg, the machine’s retail price increases an average of 3% a year. ACG can earn about 5% in a conservative invest accountt on its monthly deposits for the machine sinking fund

Determine how much must ACG deposit into the sinking fund acct at the beginning of each month to meet its machine replacement objective.

Any help will be greatly appreciated!

wat

April 27th 2006, 04:12 AM

Question:

ACG inc has purchased a new machine at a cost of 255,000. the machine is expected to have a useful life of about 10 years and no salvage value. ACG is interest in establishing a "sinking fund" for the purchase of a new machine in 10 years. Research indicates than on an avg, the machine’s retail price increases an average of 3% a year. ACG can earn about 5% in a conservative invest accountt on its monthly deposits for the machine sinking fund

Determine how much must ACG deposit into the sinking fund acct at the beginning of each month to meet its machine replacement objective.

Any help will be greatly appreciated!

Is it even a sinking fund problem?

It seems like you need to accumulate $255K at 3% for 10 years to get the price in the future, then accumulate $X at 5% for 10 years to equal that. So, it's just kinda matching two annuities up. I guess you could call it a sinking fund.

But, in short, you should try and solve:

$255,000 (1.03^10) = X * (s(double dot)_10|.05), where the bolded part is a accumulated annuity due (''', I actually forgot the name of it) over 10 years at 5%.

PistolPt01

April 27th 2006, 07:53 AM

Is the answer $2211.10 per month? :eek:

Jon Ho

April 27th 2006, 10:52 AM

hey pisolpt, can you show me how you got 2211.10? I got something similar to that and was wondering how you got yours. Thanks

PistolPt01

April 27th 2006, 11:40 AM

Sure,

The price of a new machine in ten years will be:

255,000 * (1.03)^10 = 342,698.68

So the sinking fund must equal that in order to buy one.

The terms are in MONTHS, so adjust your 5% interest rate accordingly...

(1.05)^(1/12) = 1.004074

so the interest rate you will use will be 0.4074 %

Since you know....

AV = 342,698.68

n = 120 (months)

i = 0.4074 %

The sum of all future payments must = the AV....so...

342,698.68 = X (s (double-dot) angle 120 at .4074%)

X = 2211.10

:eek:

loveitlive

May 1st 2006, 06:10 PM

One quick question, why did you all use double dot?

wat

May 1st 2006, 10:04 PM

One quick question, why did you all use double dot?

Determine how much must ACG deposit into the sinking fund acct at the beginning of each month to meet its machine replacement objective.

It's because of that line - in particular, the bolded part.

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