Ten years ago, Hailey invested $2,400 and locked in a 8 percent annual interest rate for 30 years (end 20 years from now). Aidan can make a 20-year investment today and lock in a 9 percent interest rate.
How much money should he invest now in order to have the same amount of money in 20 years as Hailey?
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
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