##### if 2000 was deposited into a savings account when you were born and that savings

label Algebra
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account_balance_wallet \$5

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

Oct 14th, 2015

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

Oct 14th, 2015

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Oct 14th, 2015
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Oct 14th, 2015
Aug 20th, 2017
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