nolan began a savings account three years ago. he invested $100 at a 2% interest rate according to the…

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. lets 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

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. lets 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

Explanation:

Step1: Find Anias's current account value

Let's assume the current year is (x) years after Nolan started. Nolan's account value is (V_N = 100(1.02)^x). Anias started 3 years later, so her account - value formula is (V_A=100(1.02)^{x - 3}).

Step2: Let's find the value of Anias's account now (when (x) is the current year).

We can rewrite (V_A = 100(1.02)^{x - 3}=\frac{100(1.02)^x}{(1.02)^3}).

Step3: Calculate ((1.02)^3)

((1.02)^3=1.02\times1.02\times1.02 = 1.061208).

Step4: Find the amount Anias would have needed to invest 3 years ago to have the same amount now

Let the amount she would have needed to invest 3 years ago be (P). We know that (P(1.02)^3=100). Then (P=\frac{100}{(1.02)^3}). Substitute ((1.02)^3 = 1.061208) into the formula: (P=\frac{100}{1.061208}\approx94.23).

Answer:

(94.23) (corresponding to the option ($94.23))