12. jack plans to deposit $500 into a new bank account that earns 2% interest compounded annually. he will…

Explanation:

Step1: Calculate simple - interest

The simple - interest formula is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Given $P=$500$, $r = 0.02$, and $t = 2$. $I_{s}=Prt=500\times0.02\times2=$20$

Step2: Calculate compound - interest

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, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years the money is invested for. $A = 500\times(1 + 0.02)^{2}=500\times1.02^{2}=500\times1.0404=$520.2$ $I_{c}=A - P=520.2-500=$20.2$

Step3: Find the difference

Find the difference between compound interest and simple interest: $I_{c}-I_{s}=20.2 - 20=$0.2$

Answer:

$$0.20$