Step-by-step explanation:
Sure, to find the capital, let's consider the formula for simple interest:
Simple Interest (\(SI\)) = \(\frac{P \times R \times T}{100}\)
Given that the interest diminishes by $900 due to a decrease in the interest rate from 12% to 10.5%, we can set up an equation to find the capital (\(P\)).
Let's denote:
Initial interest at 12% = \(SI_1\)
Interest at 10.5% = \(SI_2\)
Difference in interest = $900
Using the formula for simple interest, the initial interest (\(SI_1\)) is:
\(SI_1 = \frac{P \times 12 \times T}{100}\)
And the interest (\(SI_2\)) after the reduction to 10.5% is:
\(SI_2 = \frac{P \times 10.5 \times T}{100}\)
The difference in interest is given as $900, so the equation becomes:
\(SI_1 - SI_2 = 900\)
Substituting the expressions for \(SI_1\) and \(SI_2\):
\(\frac{P \times 12 \times T}{100} - \frac{P \times 10.5 \times T}{100} = 900\)
Now, simplify the equation to solve for \(P\), the principal (capital).
The time \(T\) is not provided, but if the time period is consistent for both calculations, we can cancel out \(T\) when solving for \(P\). Please provide the time period if available.
