infinitybenzo

TheChad
Hope the following detailed calculation explains what you are asking
Existing bond
Total market value = 5 500 000 (given)
Market value/bond = 80 (given)
Number of bonds = 68 750 = 5 500 000/ 80
Total par value = 68 750 * 100 = 6 875 000
Duration = 4 (given)
Dollar duration = 5 500 000 *4 / 100 = 220 000
New bond must have the same dollar duration, i.e., 220 000
Duration = 5 (given)
Total Market value = 220 000/5 * 100 = 4 400 000
Mkt value/bond = 90 (given)
Number of bonds = 48 889 = 4 400 000/ 90
Total par value = 48 889 * 100 = 4 888 889 (as given as answered)
Master this well since you will encounter this equal dollar duration again and again (in risk management and portfolio management)