the same amount of principal is invested in different accounts earning the same interest rate. which of the…

Explanation:

Step1: Recall interest - earning concepts

Simple interest formula is $A = P(1+rt)$ where $P$ is principal, $r$ is annual interest rate and $t = 1$ year. For annual - compounding, $A=P(1 + r)^1=P(1 + r)$. For daily - compounding, the compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, with $n = 365$ (days in a year) and $t = 1$, so $A=P(1+\frac{r}{365})^{365}$.

Step2: Analyze each option

• Option a: If no interest is earned, $A = P$.
• Option b: For simple interest, $A=P(1 + r)=P+Pr$.
• Option c: For annual compounding, $A = P(1 + r)=P+Pr$.
• Option d: The formula for daily compounding $A = P(1+\frac{r}{365})^{365}$. By the formula of compound interest, as the number of compounding periods $n$ increases, the value of $(1+\frac{r}{n})^{n}$ increases. The limit of $(1+\frac{r}{n})^{n}$ as $n\rightarrow\infty$ is $e^{r}$. Since $n = 365$ for daily compounding, it will have a higher accumulated value than simple interest and annual - compounding for the same principal $P$ and interest rate $r$.

Answer:

D. An account earning interest compounded daily