Question

Randy, a student, has $500 to deposit in a new checking account, but Randy knows he will not be able to maintain a minimum balance. He will not use an ATM card, but will write a large number of checks. Randy is trying to choose between the unlimited check writing offered by South Trust and the low per-check fee offered by Sun Coast. How many checks would Randy have to write each month for the account at South Trust to be the better option?

South Trust Bank Sun Coast Bank

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ATM Charges:

Home bank Free Free

Other bank $1.25 per use $1.25 per use

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Checking:

Minimum deposit $1 $1

Minimum balance required to

avoid fees $500 N/A

Monthly fees $11.00 $2.50

Check-writing charges Unlimited Each check 50 cents

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*N/A means monthly fees apply irrespective of account balances.

For the account at South Trust Bank to be the better option, the number of checks Randy would need to write each month is ______. (Round to the nearest whole number.)

Answer 1

As Randy is not going to use ATM service and charges are same in both of the banks. So, it is irrelevant for decision making. Also Randy is not going to maintain minimum balance and charges for not maintaining minimum balace are also same in both options. So it is also not relevant for decision making.

First calculate the break even position in cheque drawing between both the banks: Fixed + variable cost of both banks must be equal at break even point. So,

Let the number of cheques drwan be x. then,

Total monthly charges of South trust bank for x number of cheques = $11 + 0*x = $11

Total monthly charges of Sun coast bank for x number of cheques = $2.50 + $0.5*x

At break even both should be equal. then,

$11 = $2.50 +$0.5*x

0.5*x = $8.5

x = 17 cheques.

So, the number of cheques to be drawn of south trust bank to be a better option must not be less than 17 per month.