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

Explanation:

Step1: Recall interest - earning concepts

An account earning no interest will have only the principal amount at the end of the year.

Step2: Consider simple - interest formula

The formula for simple interest is $A = P(1 + rt)$, where $P$ is the principal, $r$ is the annual interest rate, and $t = 1$ year. So $A=P(1 + r)$.

Step3: Consider annual - compounding formula

The formula for compound interest compounded annually is $A = P(1 + r)^t$. With $t = 1$, $A = P(1 + r)$.

Step4: Consider daily - compounding formula

The formula for compound interest compounded $n$ times a year is $A=P(1+\frac{r}{n})^{nt}$. For daily compounding, $n = 365$ and $t = 1$, so $A = P(1+\frac{r}{365})^{365}$. Since $(1+\frac{r}{365})^{365}>1 + r$ (by the property of the exponential - like function $y=(1+\frac{a}{x})^x$ which approaches $e^a$ as $x$ increases and for $x = 365$ and positive $a=r$), the account earning interest compounded daily will have the greatest accumulated value.

Answer:

D. An account earning interest compounded daily