Ten years ago, Hailey invested $2,100 and locked in an annual interest rate of 8 percent for 30 years (ending 20 years from now). Aidan can make a 20-year investment today and lock in an interest rate of 9 percent. How much money should he invest now in order to have the same amount of money in 20 years as Hailey? (

$3,770.53

Explanation:

Given data;

Amount Hailey invested = $2,100

annual interest rate = 8 Percent for 30 years ending 20 years from now

Aidan can make an investment for 20 years at 9 percent.

To determine how much money Aidan should invest in order to have the same amount of money in 20 years as Hailey =

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

FV20 = PV -10 × (1 + i)³⁰

FV20 = $2,100 × (1 + 0.08)³⁰

= $2,100 × 10.06266

= $21,131.59

Therefore, Aidan will have to deposit:

PV = FV20 ÷ (1 + i)N

PV = $21,131.59 ÷ (1 + 0.09)²⁰

= $21,131.59 ÷ 5.60441

= $3,770.53

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