If the simple interest on Re. 1 for 1 month is 1 paisa, then the rate per cent per annum will be

The correct option is 12%.

Let us break down the problem step-by-step to understand how we arrive at this rate per cent per annum.

Step 1: Understand the given values
The principal amount ($P$) is given as Re. 1.
Since the interest is given in paisa, let us convert the principal into paisa for convenience. We know that:
Re. 1 = 100 paise.
Therefore, Principal ($P$) = 100 paise.

The simple interest ($\mathrm{SI}$) is given as 1 paisa.
Therefore, $\mathrm{SI}$ = 1 paisa.

The time period ($T$) is given as 1 month.
Since the rate of interest is required "per annum" (yearly), we must convert the time from months to years. We know that 1 year has 12 months.
Therefore, Time ($T$) = $\frac{1}{12}$ years.

Step 2: Apply the Simple Interest Formula
The standard formula for calculating Simple Interest is:
$\mathrm{SI}=\frac{P\times R\times T}{100}$
where:
• $\mathrm{SI}$ is the Simple Interest,
• $P$ is the Principal amount,
• $R$ is the Rate of interest per cent per annum, and
• $T$ is the Time in years.

Step 3: Calculate the Rate of Interest ($R$)
Substituting the known values into the formula, we get:
$1=\frac{100\times R\times \frac{1}{12}}{100}$

We can simplify the right-hand side of the equation by canceling out the 100 in the numerator and the denominator:
$1=R\times \frac{1}{12}$

To solve for $R$, we multiply both sides of the equation by 12:
$R=12$

Thus, the rate of interest is 12% per annum.