Multiple choice

Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w?

  1. $\displaystyle \frac { w }{ 1+1.08 } $
  2. $\displaystyle \frac { w }{ 1.08+1.16 } $
  3. $\displaystyle \frac { w }{ 1.16+1.24 } $
  4. $\displaystyle \frac { w }{ 1.08+{ \left( 1.08 \right) }^{ 2 } } $
  5. $\displaystyle \frac { w }{ { \left( 1.08 \right) }^{ 2 }+{ \left( 1.08 \right) }^{ 3 } } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

After 1 year, the account has x * 1.08. Then another x is added, so the balance is x * 1.08 + x. After the second year, this amount earns 8% interest: (x * 1.08 + x) * 1.08 = w. So, w = x * (1.08^2 + 1.08). Therefore, x = w / (1.08^2 + 1.08).

AI explanation

After two years, the first deposit of x dollars grows to 1.08^2 * x dollars. The second deposit of x dollars, made after one year, grows to 1.08 * x dollars by the end of the second year. Therefore, the total amount w equals x * (1.08^2 + 1.08). Solving for x, we get x = w / (1.08 + 1.08^2).

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