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A bank has two, 3-year commercial loans with a present value of $70 million. The first...

A bank has two, 3-year commercial loans with a present value of $70 million. The first is a $30 million loan that requires a single payment of $37.8 million in 3 years, with no other payments until then. The second is for $40 million. It requires an annual interest payment of $4 million. The principal of $40 million is due in 3 years. The general level of interest rates is 6%. What is the duration of the bank’s commercial loan portfolio?

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Answer #1

Duration of First loan = 3 Years (because it has not interest payments in between

Duration of Second Loan = 2.75 Years

Duration of Commercial Loan Portfolio = weight of first loan * Duration of First Loan + weight of Second loan * Duration of Second Loan

Duration of Commercial Loan Portfolio = (3/7) * 3 + (4/7) * 2.75

Duration of Commercial Loan Portfolio = 2.86 Years

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