which of the following ways to compute interest on a savings account with $1,000 paying 2% will yield the…

Answer:

C. Interest compounded monthly.

Explanation:

Step1: Recall interest - rate formulas

Simple interest formula: $A = P(1+rt)$, compound - interest formula: $A=P(1 + \frac{r}{n})^{nt}$, where $P=$1000$, $r = 0.02$, and assume $t = 1$ year.

Step2: Analyze simple interest

For simple interest, $A_{s}=P(1+rt)=1000(1 + 0.02\times1)=1000\times1.02=$1020$.

Step3: Analyze semi - annual compounding

For semi - annual compounding ($n = 2$), $A_{1}=P(1+\frac{r}{n})^{nt}=1000(1+\frac{0.02}{2})^{2\times1}=1000(1 + 0.01)^{2}=1000\times1.01^{2}=1000\times1.0201=$1020.1$.

Step4: Analyze monthly compounding

For monthly compounding ($n = 12$), $A_{2}=P(1+\frac{r}{n})^{nt}=1000(1+\frac{0.02}{12})^{12\times1}\approx1000(1+0.00167)^{12}\approx1000\times1.02018=$1020.18$.

Step5: Analyze quarterly compounding

For quarterly compounding ($n = 4$), $A_{3}=P(1+\frac{r}{n})^{nt}=1000(1+\frac{0.02}{4})^{4\times1}=1000(1 + 0.005)^{4}=1000\times1.005^{4}=1000\times1.02015=$1020.15$. Since $1020<1020.1<1020.15<1020.18$, interest compounded monthly yields the most money.