A bond with a duration of five is currently priced at $103.

The approximate price change of a bond due to a change in interest rates can be estimated using the formula:

Price Change (%)=−Duration×ΔInterest Rate\text{Price Change (\%)} = - \text{Duration} \times \Delta \text{Interest Rate} Price Change (%) = −Duration × ΔInterest Rate

Given:

Duration = 5

Current Price = $103

Change in Interest Rate ( Δ\Delta Δ ) = 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. $108.15 and B. $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.