if 2000 was deposited into a savings account when you were born and that savings account earns 5.0% each year how much money will be account when you turn 18

Thank you for the opportunity to help you with your question!

Hi SK,

Because of how the problem is stated, I assume that interest is earned only once a year.

I'll first show the process, then give the equation that allows you to calculate the answer.

Let V(n) = value of the account AFTER n years.

V(1) = 2000 + 2000 * 0.05 = 2000 * (1 + 0.05) = 2000 * 1.05

V(2) = V(1) + V(1) * 0.05 = V(1) * 1.05 = 2000 * (1.05) * (1.05) = 2000 * (1.05)^2

V(3) = V(2) + V(2) * 0.05 = V(2) * 1.05 = [V(1) * 1.05] * 1.05 = V(1) * (1.05)^2 = 20000 * (1.05)^3

More generally.

V(n) = 2000 * (1.05)^n

For this problem, n = 17 (since it is 17 years after birth that you have your 18th birthday), so

V(17) = 2000 * (1.05)^17

Using a calculator, there will be V(17) ~ 2000 * 2.292 = 4584.00

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