Calculating and Comparing Simple and Compound Interest(TEKS.Math.8.12.D)

Simple: $I=prt=1000(0.05)(8)=400$ (amount $1400$). Compound: $A=p(1+r)^t=1000(1.05)^8\approx1477.46$, so interest $\approx477.46$. Difference $=477.46-400=77.46$, and compound earns more. Compound grows faster because interest earns interest; this advantage increases with higher $r$ and longer $t$, which is why most investments use compounding.

Simple: $I=prt=500(0.03)(6)=90$ (amount $590$). Compound: $A=500(1.03)^6\approx500(1.194052)=597.03$, so interest $\approx97.03$. Compound earns about \$7.03$ more. Because $A=p(1+r)^t$ grows multiplicatively, the compound advantage increases with higher $r$ and longer $t$; real-world investments typically use compounding.

Simple: $I=prt=1200(0.04)(10)=480$, total $=1680$. Compound: $A=1200(1.04)^{10}\approx1200(1.480244)=1776.29$. Difference $=1776.29-1680=96.29$. Compound is larger because interest itself earns interest; the gap widens as $r$ or $t$ increase, which is why investments usually compound.

Simple: $I=prt=2000(0.09)(4)=720$. Compound: $A=2000(1.09)^4\approx2000(1.411582)=2823.16$, so interest $\approx823.16$. Thus compound interest is larger. Because compounding uses $A=p(1+r)^t$, its advantage grows with higher $r$ and longer $t$, which is why most investments compound.

Simple: $I=prt=750(0.06)(3)=135$. Compound: $A=750(1.06)^3\approx750(1.191016)=893.26$, so interest $\approx143.26$. Difference $=143.26-135=8.26$. Compound pays more because interest earns interest; the advantage increases with larger $r$ and longer $t$, which is why most real accounts compound.