for Chapter 30 problem 27 of corporate finance by brealey

where did it get the formulas to solve the problem. I cant find it anywhere.How did you arrive with this formulas to solve the problem? Pls help. Thanks

Daily interest = (1 + Annual interest) 1/ Number of days in a year -1

Increase in the cost = Cost of wire transfer - Cost of depository transfer

Increase in cost = Interest ratex Number of days reduced Size of collection

A parent company settles the collection account balances of its subsidiaries once a week. (That is, each week it transfers any balances in the accounts to a central account.) The cost of a wire transfer is $10. A check costs $.80. Cash transferred by wire is available the same day, but the parent must wait three days for checks to clear. Cash can be invested at 12% per year. How much money must be in a collection account before it pays to use a wire transfer? Daily interest = (1 + Annual interest) Number of days in a year - 1 a = (1+12%) - 1365 = 0.03105% Hence, the increase in the cost is $9.2. Compute the increase in the cost of wire transfer using the equation as shown below: Increase in the cost = Cost of wire transfer - Cost of depository transfer = $10-$0.8 = $9.2 Hence, the increase in the cost is $9.2. Compute the size of the collection account before it pays to use a wire transfer using the equation as shown below: Increase in cost = Interest rate x Number of days reduced Size of collection $9.2 = 0.03105%x3x Size of collection $9.2 = 0.09315%Size of collection Solving the above equation: $9.2 Size of collection 0.09315% = $9,876.54 Hence, the size of the collection is $9,876.54 A parent company settles the collection account balances of its subsidiaries once a week. (That is, each week it transfers any balances in the accounts to a central account.) The cost of a wire transfer is $10. A check costs $.80. Cash transferred by wire is available the same day, but the parent must wait three days for checks to clear. Cash can be invested at 12% per year. How much money must be in a collection account before it pays to use a wire transfer? Daily interest = (1 + Annual interest) Number of days in a year - 1 a = (1+12%) - 1365 = 0.03105% Hence, the increase in the cost is $9.2. Compute the increase in the cost of wire transfer using the equation as shown below: Increase in the cost = Cost of wire transfer - Cost of depository transfer = $10-$0.8 = $9.2 Hence, the increase in the cost is $9.2. Compute the size of the collection account before it pays to use a wire transfer using the equation as shown below: Increase in cost = Interest rate x Number of days reduced Size of collection $9.2 = 0.03105%x3x Size of collection $9.2 = 0.09315%Size of collection Solving the above equation: $9.2 Size of collection 0.09315% = $9,876.54 Hence, the size of the collection is $9,876.54