which interest rate will earn the largest return on $1,000?\na. simple interest at 5 percent\nb. compound…

which interest rate will earn the largest return on $1,000?\na. simple interest at 5 percent\nb. compound interest at 5 percent\nc. compound interest at 3 percent\nd. simple interest at 3 percent

which interest rate will earn the largest return on $1,000?\na. simple interest at 5 percent\nb. compound interest at 5 percent\nc. compound interest at 3 percent\nd. simple interest at 3 percent

Answer

Explanation:

Step1: Recall interest - rate formulas

Simple interest formula: $I = Prt$, where $P=$1000$ is the principal, $r$ is the interest rate, and $t$ is the time. For simplicity, assume $t = 1$ year. For option A, $I_A=1000\times0.05\times1 = 50$, for option D, $I_D=1000\times0.03\times1=30$.

Step2: Recall compound - interest formula

Compound - interest formula: $A = P(1 + r)^t$, where $P = 1000$, $r$ is the interest rate, and $t$ is the number of years. Assume $t = 1$ year. For option B, $A_B=1000(1 + 0.05)^1=1000\times1.05 = 1050$, interest $I_B=1050 - 1000=50$. For option C, $A_C=1000(1 + 0.03)^1=1000\times1.03 = 1030$, interest $I_C=1030 - 1000 = 30$. When $t>1$, compound interest at 5% will be greater than simple interest at 5% because compound interest takes into account interest on previously - earned interest.

Answer:

B. Compound interest at 5 percent