Let X represent the amount of the loan and .15X represent the amount of the compensating deposit. We need X (the amount of the loan) minus .15X (the amount of the compensating deposit) to be equal to $150,000. The equation and its solution are: X ? .15X = $150,000 .85X = $150,000 X = $176,471 The problem could also be solved by dividing $150,000 by .85 (1.00 ? .15).
This is $150,000 ÷ 1.15. The resulting amount is not a reasonable answer to the question. A portion of the loan proceeds will not be available to Keller, because it will be used to cover the compensating deposit requirement. Therefore, Keller will have to borrow more than $150,000 in order to have $150,000 available after subtracting 15% of the loan amount. $130,435 is less than $150,000, so a loan of $130,435 amount could not possibly provide the funds Keller needs and the funds to cover the compensating deposit required.
This is $150,000 ÷ .77. This would be correct if this were a discounted note, discounted at its interest rate of 8% and neither the interest amount nor the compensating balance required were available to the borrower. However, this is not a discounted note. Only the compensating balance required will not be available to the borrower.
This is $150,000 × 1.15. Multiplying by 1.15 effectively calculates 15% of $150,000 and adds that to $150,000. However, $150,000 is how much Keller needs from the loan. The bank will calculate the amount of the compensating balance requirement on the amount borrowed instead. The amount borrowed will need to include the compensating balance requirement.
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