the same amount of principal is invested in d...

# Explanation: ## Step1: Recall interest - accumulation formulas Let the principal be $P$, the annual interest rate be $r$. For an account earning no interest, the accumulated value $A_1 = P$. For simple - interest, the formula is $A_2=P(1 + r)$ (where the time $t = 1$ year). For annual compounding, the formula is $A_3=P(1 + r)$ (since $n = 1$ compounding period in a year, and the compound - interest formula is $A=P(1+\frac{r}{n})^{nt}$, with $t = 1$ and $n = 1$). For daily compounding, $n = 365$ (assuming a non - leap year), and $A_4=P(1+\frac{r}{365})^{365}$. ## Step2: Compare the values We know that the function $y=(1+\frac{r}{n})^{n}$ is an increasing function of $n$ for positive $r$. As $n$ increases from $1$ (annual compounding) to $365$ (daily compounding), the value of $(1+\frac{r}{n})^{n}$ increases. Also, $P(1 + r)<P(1+\frac{r}{365})^{365}$ for $r>0$. And $P$ (no - interest account) and $P(1 + r)$ (simple - interest and annual - compounding) are less than $P(1+\frac{r}{365})^{365}$. # Answer: D. An account earning interest compounded daily