The following is an FI's balance sheet ($millions). Notes to Balance Sheet: Munis are 2-year 6 percent annual coupon municipal notes selling at par. Loans are floating rates, repriced quarterly. Spot discount yields for 91-day Treasury bills are 3.75 percent. GICs are 1-year pure discount certificates of deposit paying 4.75 percent.
What is the duration of the municipal notes (the value of x)?

Question

The following is an FI's balance sheet ($millions).  Notes to Balance Sheet: Munis are 2-year 6 percent annual coupon municipal notes selling at par. Loans are floating rates, repriced quarterly. Spot discount yields for 91-day Treasury bills are 3.75 percent. GICs are 1-year pure discount certificates of deposit paying 4.75 percent.
What is the duration of the municipal notes (the value of x)?

Quizplus · Accepted Answer

To calculate the duration of municipal notes, we need to use the modified duration formula. Modified duration = (1 + yield/number of payments) / (1 + yield/number of payments + coupon rate/number of payments) * time to maturity. Plugging in the values given in the problem, we get:

Modified duration = (1 + 0.06/1) / (1 + 0.06/1 + 0.06/1) * 2
= 1.03 / 1.12 * 2
= 1.94 years.

Therefore, the correct answer is A) 1.94 years.

The Following Is an FI's Balance Sheet ($Millions)