Question

9,600 dollars is placed in a savings account with an annual interest rate of 1.2%. if no money is added or removed from the account, which equation represents how much will be in the account after 5 years? answer \\( m = 9,600(0.988)^5 \\) \\( m = 9,600(0.012)^5 \\) \\( m = 9,600(1 - 0.012)^5 \\) \\( m = 9,600(1.012)^5 \\)

Explanation:

Step1: Recall compound interest formula

The standard formula for compound interest (with annual compounding, no additional deposits/withdrawals) is $M = P(1 + r)^t$, where $P$ is principal, $r$ is annual interest rate (decimal), $t$ is time in years.

Step2: Convert rate to decimal

Annual rate $1.2\% = \frac{1.2}{100} = 0.012$

Step3: Substitute values into formula

$P = 9600$, $r = 0.012$, $t = 5$. Substitute: $M = 9600(1 + 0.012)^5 = 9600(1.012)^5$

Answer:

$M = 9,600(1.012)^5$