calc:

Hailey

n=30, i=8, pv=-2,400, pmt=0, cpt fv

=24,150.38

Aidan

n=0, i=9, pmt=0, fv=-24,150.38, cpt pv

= 4,309.17

hand:

First, determine how much Hailey will have 20 years from now:

FV20 = PV -10 × (1 + i)30

FV20 = $2,400 × (1 + 0.08)30

= $2,400 × 10.06266

= $24,150.38

So, Aidan will have to deposit:

PV = FV20 / (1 + i)N

PV = $24,150.38 / (1 + 0.09)20

= $24,150.38 / 5.60441 = $4,309.17 ;