Certainly! Let's solve this step-by-step:
1. Identify the initial rate and the new rate:
The initial rate of interest is [tex]\(8 \%\)[/tex], and the new rate of interest is [tex]\(10 \%\)[/tex].
2. Calculate the absolute increase in rate:
The increase in the rate is calculated as:
[tex]\[
\text{Increment} = \text{New Rate} - \text{Initial Rate} = 10\% - 8\% = 2\%
\][/tex]
3. Determine the increment percent:
We need to find out how much the increment of [tex]\(2 \%\)[/tex] represents compared to the initial rate of [tex]\(8 \%\)[/tex]. The formula to calculate the increment percent is:
[tex]\[
\text{Increment Percent} = \left( \frac{\text{Increment}}{\text{Initial Rate}} \right) \times 100
\][/tex]
Substituting the known values:
[tex]\[
\text{Increment Percent} = \left( \frac{2}{8} \right) \times 100 = 0.25 \times 100 = 25\%
\][/tex]
So, the increment percent when the rate of interest increases from [tex]\(8 \%\)[/tex] to [tex]\(10 \%\)[/tex] is [tex]\(25 \%\)[/tex].
Thus, the correct answer is:
c. [tex]\(25 \%\)[/tex]
