Question

Nolan began a savings account three years ago. He invested $100 at a 2% interest rate according to the equation Vn = 100(1.02)x, where Vn is the value of his account after x years. Anias started an account today. She invested $100 at a 2% interest rate according to the equation Va = 100(1.02)x–3, where Va is the value of her account. Let’s say Anias started saving at the same time Nolan did, three years ago. Approximately how much money would she have had to invest to have the same amount of money she has now?
$5.77
$90.24
$94.23
$106.12

Answer 1

Anias currently has $100 (since Va = 100(1.02)^{3-3} = 100). If she had invested that amount 3 years ago it would have grown by (1.02)^3, so the required initial investment P satisfies P(1.02)^3 = 100. Thus

P = 100 / (1.02)^3 ≈ 100 / 1.061208 ≈ $94.23.

Answer: $94.23