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Gold Loan

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A bank offers a corporate client a choice between borrowing cash at 11% per annum and borrowing gold at 2% per annum. (If gold is borrowed, interest must be repaid in gold. Thus, 100 ounces borrowed today would require 102 ounces to be repaid in one years time.) The risk-free interest rate is 9.25% per annum and storage costs are 0.5% per annum. The interest rates on the two loans are expressed with annual compounding. The risk-free interest rate and storage costs are expresses with continuous compounding. Discuss whether the rate of interest on the gold loan is too high or too low in relation to the rate of interest on the cash loan.

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Solution Summary

The solution calculates and compares the rate of interest on cash loan and gold loan.

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If $100 cash is borrowed the amount that has to be returned at the end of year 1=$100*(1+11%) = $111
Cost of borrowing cash=$111-$100=$11

If someone borrows gold he will convert it to cash and use it. At the end of year 1 he will buy gold from the market and return it to the bank.
Price of gold will depend on the risk free rate and the ...

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