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A $1,000 six-year bond has an 8 percent coupon and contracts to make annual payments of interest. The duration of this bond is 4.99 years. The current interest rate is 8.0 percent. What will be the new price using the duration model if interest rates increase to 8.5 percent? A.$976.90.B.$23.10.C.$977.23.D.-$23.10.E.$1,023.10.

Question

A 1,000six−yearbondhasan8percentcouponandcontractstomakeannualpaymentsofinterest.Thedurationofthisbondis4.99years.Thecurrentinterestrateis8.0percent.Whatwillbethenewpriceusingthedurationmodelifinterestratesincreaseto8.5percent? A.1,000 six-year bond has an 8 percent coupon and contracts to make annual payments of interest. The duration of this bond is 4.99 years. The current interest rate is 8.0 percent. What will be the new price using the duration model if interest rates increase to 8.5 percent? A.976.90.B.23.10.C.23.10.C.977.23.D.-23.10.E.23.10.E.1,023.10.

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Solution

The correct answer is A. $976.90.

Here's a step-by-step explanation:

  1. Duration is a measure of the sensitivity of the price of a bond to changes in interest rates. The duration of this bond is given as 4.99 years.

  2. The formula to calculate the change in bond price using duration is: ΔP/P = -D*(Δi), where ΔP/P is the percentage change in price, D is the duration, and Δi is the change in interest rate.

  3. The change in interest rate (Δi) is the new interest rate minus the old interest rate. In this case, it's 8.5% - 8.0% = 0.005 (or 0.5% when expressed as a decimal).

  4. Plugging these values into the formula gives: ΔP/P = -4.99 * 0.005 = -0.02495, or -2.495% when expressed as a percentage.

  5. This means the bond price will decrease by 2.495%. To find the new price, subtract this percentage from the original price of 1,000:1,000: 1,000 - (1,000∗0.02495)=1,000 * 0.02495) = 975.05.

However, the closest answer choice to this calculated value is A. $976.90. This discrepancy could be due to rounding errors or slight differences in the way the duration was calculated.

This problem has been solved

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