On July 1, Dichter Company obtained a $2,000,000, 180-day bank loan at an annual rate of 12%. The loan agreement requires Dichter to maintain a $400,000 compensating balance in its checking account at the lending bank. Dichter would otherwise maintain a balance of only $200,000 in this account. The checking account earns interest at an annual rate of 6%. Based on a 360-day year, the effective interest rate on the borrowing is

The annual effective  interest rate based on a 360 day period is 12.67%

Explanation:

The effective interest rate for a 180 day borrowing period is the ratio of net interest cost  to net available proceeds.

The net interest cost = the gross interest cost -  the incremental interest revenue.

The gross interest cost =  $2,000,000 × 12% × (6  months ÷ 12 months) = $2,000,000 × 0.12 × 0.5 = $120,000

the incremental interest revenue =  $200,000 × 6% ×  (6 months ÷ 12 months) = $200,000 × 0.06 ×  0.5= $6,000

Since the net interest cost = the gross interest cost -  the incremental interest revenue

Net interest cost =  $120,000 - $6,000 = $114,000

net available proceeds = $2000000 - $200000 = $1800000

Therefore, the  effective interest rate based om a 180 day period = net interest cost/net available proceeds = $114,000 / $1,800,000 = 0.0633 = 6.33%

The annual effective  interest rate based on a 360 day period = 6.33% × 2 = 12.67%

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