The approximate price change of a bond due to a change in interest rates can be estimated using the formula:
Price Change (%)=#Duration×#Interest Rate\text{Price Change (\%)} = - \text{Duration} \times \Delta \text
{Interest Rate}Price Change (%)=#Duration×#Interest Rate
Given:
* Duration= 5
* Current Price= $103
* Change in Interest Rate(#\Delta#) = 2% or 0.02
Price Change (%)=#5×0.02=#0.10 (#10%)\text{Price Change (\%)} = -5 \times 0.02 = -0.10 \, (-10\%) Price Change (%)=#5×0.02=#0.10(#10%) The new price is calculated as:
New Price=Current Price×(1+Price Change)=103×(1#0.10)=103×0.90=97.85\text{New Price} = \text
{Current Price} \times (1 + \text{Price Change}) = 103 \times (1 - 0.10) = 103 \times 0.90 = 97.85 New Price=Current Price×(1+Price Change)=103×(1#0.10)=103×0.90=97.85
* A. $108.15andB. $113.30: These represent price increases, which are incorrect for rising interest rates.
* D. $92.70: This reflects a greater-than-actual price drop, which is inconsistent with the duration-based calculation.