A certain amount earns simple Interest of Rs. 1,750/- after 7 years. Had the interest been 2% more, how much more interest would it have earned ?
A certain amount earns simple Interest of Rs. 1,750/- after 7 years. Had the interest been 2% more, how much more interest would it have earned ?
To find out how much more interest would have been earned if the interest rate were 2% more,
we need to calculate the interest earned at the original rate and the interest earned at the increased rate.
Let's denote: - Original interest rate = \(R\) (in percentage)
- Principal amount = \(P\)
- Time period = \(T\) (in years)
- Original interest earned = \(I_1\)
- Interest earned at the increased rate = \(I_2\)
Given: - \(I_1 = Rs. 1,750\) - \(T = 7\) years We can use the formula for simple interest: \[I = \frac{P \times R \times T}{100}\] For the original interest rate: \[1750 = \frac{P \times R \times 7}{100}\] \[P \times R = \frac{1750 \times 100}{7}\] \[P \times R = 25000\] Now, if the interest rate were increased by 2%, the new rate would be \(R + 2\) (in percentage). For the increased interest rate: \[I_2 = \frac{P \times (R + 2) \times 7}{100}\] The difference in interest would be: \[\text{Difference} = I_2 - I_1\] Let's calculate \(I_2\) and the difference: \[I_2 = \frac{P \times (R + 2) \times 7}{100}\] \[= \frac{P \times (R \times 7 + 2 \times 7)}{100}\] \[= \frac{P \times (25000 + 2 \times 7)}{100}\] \[= \frac{P \times (25000 + 14)}{100}\] \[= \frac{P \times 25014}{100}\] \[= 250.14P\] Now, calculate the difference: \[\text{Difference} = I_2 - I_1\] \[= 250.14P - 1750\] We have the value of \(P\) from the earlier calculation: \[P \times R = 25000\] \[R = \frac{25000}{P}\] Substitute this value of \(R\) into the difference equation: \[\text{Difference} = 250.14P - 1750\] \[= 250.14P - 1750\] \[= 250.14 \times \frac{25000}{R} - 1750\] Now, we need to determine the value of \(R\) (original interest rate). However, it's not given, so we can't determine the exact difference. Therefore, the answer is option D: Cannot be determined.
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