Question

you deposit $7,000 in a bank account that earns 2% compound interest annually.
what is the value of your $7,000 in four years?
$7,560
$7,577
$6,423
$6,440

Explanation:

Step1: Recall compound interest formula

The compound interest formula is $A = P(1 + r)^t$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years.
Here, $P = 7000$, $r = 2\% = 0.02$, and $t = 4$.

Step2: Substitute values into the formula

Substitute $P = 7000$, $r = 0.02$, and $t = 4$ into the formula $A = P(1 + r)^t$.
So, $A = 7000(1 + 0.02)^4$.

Step3: Calculate $(1 + 0.02)^4$

First, calculate $1 + 0.02 = 1.02$. Then, calculate $1.02^4$.
$1.02^4 = 1.02\times1.02\times1.02\times1.02$.
$1.02\times1.02 = 1.0404$.
$1.0404\times1.02 = 1.061208$.
$1.061208\times1.02 = 1.08243216$.

Step4: Calculate $A$

Now, multiply $7000$ by $1.08243216$.
$A = 7000\times1.08243216 = 7577.02512$. Rounding to the nearest dollar, we get $7577$.

Answer:

$7,577$ (corresponding to the option with $7,577$)