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Business Book Publishing needs to borrow $700,000 in order to finance its new inventory. Two banks...

Business Book Publishing needs to borrow $700,000 in order to finance its new inventory. Two banks were considering offered different annual loan terms: Marine Bank offered a 10% loan with a 15% compensating balance to be paid back in quarterly payments. McLean National Bank offered Business Book Publishing a 12% loan to be paid back semi-annually. Which loan terms should Business Book Publishing take?

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For the first option, the 10% quarterly payment can be converted into an annual rate using this equation: r = (1 + i/n)^(n) - 1 r is the effective rate n is the number of compounding periods per year i is the stated rate r = (1 + 10%/4)^(4) - 1 r = 10.381% However to further complicate things, the bank requires a compensatory balance of 15%. This means that the company will still pay the 10.381% rate, but will effectively only be able to borrow $700,000 - 15% as the bank requires that this money be set aside. 15% of 700000 is 105,000. So to determine the effective interest rate we must first subtract 105k from 700k, then figure out the rate. 700,000 - 105,000 = 595,000 700,000 * 10.381% = 72667 72667 / 595,000 = 12.213% For option 2 we just need to convert the 12% semiannual payment to an annual rate: r = (1 + 12%/2)^2 - 1 r = 12.36% Despite the compensatory balance and the quarterly rate, option 1 is still a lower interest rate.


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