Faircross Farms harvests its crops four times annually and receives payment for

Question

Faircross Farms harvests its crops four times annually and receives payment for its crop 3 months after it is picked and shipped. However, planting, irrigating, and harvesting must be done on a nearly continual schedule. The firm uses 3-month bank notes to finance its operations. The firm arranges an 11 percent discount interest loan with a 20 percent compensating balance four times annually. What is the effective annual interest rate on the loan? Note that the 11 percent stated interest rate is per year.

Explanation / Answer

First we will calculate effective anual interest rate for compensating balance

EAR i= (1+r/m)^m-1

Where r = R/100 and i = I/100; r and i are interest rates in decimal form. m is the number of compounding periods per year. The effective annual rate is the actual interest rate for a year.

=(1+0.2/4)^4-1

i=21.55%

Let us say principal amount is $100000

Nominal interest is $100000*0.11 =$11000

Now Annual compensatrory balance =$100000*0.2155

=$21550

Subtarct above compensatory balance from principal= $100000-$21550

=$78450

Effective interest rate=11000/78450=14.02%

Note: Here only compensating balance is assumed to be four times annualy and not 11% discount int loan. If we consider discount loan also 4 times then formula will change as below

Effective annual discount int loan = (1+0.11/4)^4-1

Effective annual rate= 11.46%

So nominal interest=$11460

Effective annual interest rate on loan=$11460/78450=14.61%

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