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?

Answer 1

Answer:

The required amount is $94.23.

Step-by-step explanation:

It is given that Nolan began a savings account three years ago and the value of his account after x years is

$V_n=100(1.02)^x$

Anias started an account today and the value of her account is

$V_a=100(1.02)^{x-3}$

We have to find the amount of money that would she have had to invest to have the same amount of money she has now.

Let the required amount be P.

If Anias started saving x amount in the savings account three years ago, then today the value of her account is

$V_a=P(1.02)^3$

The current value is 100.

$100=P(0.0612)$

Divide both sides by 0.0612.

$\frac{100}{0.0612}=P$

$94.2322=P$

$P\approx 94.23$

Therefore the required amount is $94.23.