Question

Bank A offers loans with a 10 percent stated annual rate and a 10 percent compensating balance. You wish to obtain $250,000 in a six-month loan. How much must you borrow to obtain $250,000 in usable funds? Assume you do not have any funds on deposit at the bank. What is the effective annual rate on a six-month loan? How much must you borrow to obtain $250,000 in usable funds if you currently have $10,000 on deposit at the bank? What is the effective annual rate on a six-month loan? How much must you borrow to obtain $250,000 in usable funds if you have $30,000 deposited at the bank? Excel spread would be appreciated.

Answer 1

Now the amount that you want is $ 250000 in a six-month loan. The annual stated interest is 10% or 5% for six months and 10% is the compensating balance. Here we want $ 250000 on hand, so this would be after compensating balance to be maintained with Bank A. Hence the fund to be borrowed would be ($250000*100)/90 = $ 277777.78. The interest on this would be $277777.78*5% = $ 13888.89. The annual rate on a six-month loan would be = Interest/Compensating amount = $13888.89/$250000 = 5.56% for six months and 11.1% yearly

If we have $ 10000 on deposit at the bank so the amount we would require is $240000. Hence the loan to be taken would be $240000*100/90 = $ 266666.67. Interest for six months would be $ 13,333.33. Annual effective rate would be ($13,333.33/$240000)*2 = 11.1%

If we have $ 30000 on deposit at the bank so the amount we would require is $220000. Hence the loan to be taken would be $220000*100/90 = $ 244444.44. Interest for six months would be $ 12,222.22. Annual effective rate would be ($12,222.22/$220000)*2 = 11.1%