Cash Management: Dome has a credit sale of $ 144000 yearly

Problem 1:
Dome has a credit sale of $ 144000 yearly with credit term of net 30 days,which is also the average collection period.If Dome offers a 2% discount for payment in 10 days and every customer took advantage of the new term,what would the average receivable balance be? use the full sales of $144000 for your calculation of receivable.
b)Assume the new trade term of 2/10,net 30 will increase by 15% because the discount makes Dome's price competitive.If Dome earns 20 % on sales before discounts ,should it offer the discount ?

What i did is:
annual average sales $144000
/360
.-------------------
400
net 30days x 30
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Aver.A/R Bal. $12000

Average daily credit sales $400
net 10 days sale x 10
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$4000

Acc/R Balance by $ 12000-$4000 = $ 8000
x 10%
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Annual cost $ 800

$ 144000 x 2% = $ 2880 reduce

if Dome earns 20% on sale before discounts .it should not be offer.

Problem 2

Neon Light Company of Kansas city ships lamps and lighting appliances throughout the country.Ms Neon has determined that through the establishment of local collection centers around the country, she can speed up the collection of payments by one and one days. Furthermore, the cash management department of her bank has indicated to her that she can differ her payment on her accounts by one-half day without offending suppliers. The bank has a remote disbursement center in Florida.
a) if Neon Light Company has $2 million per day in collections and $1million per day in disbursements ,how many dollars will the cash management system free up?
b) If Neon Light Company can earn 9% per annum on freed-up funds ,how much will the income be ?
c) If the total cost of the new system is $ 375000 ,should it be implemented?

My solution is :

a)
$ 2000000 x 1.5 = $ 3000000
Disbursement $ 1000000
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cash system freed up $ 4000000

b)-income = $ 4000000 x 9% = $360000

c)- if the cost of the new system is $ 375000 , it should not be implemented.