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The compound interest on a certain sum for 2 years is Rs. 756 and Simple interest is Rs. 720. If the sum is invested such that the SI is Rs. 900 and the number of years is equal to the rate percent per annum, find the rate percent?
- a)10%
- b)12%
- c)5%
- d)15%
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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The compound interest on a certain sum for 2 years is Rs. 756 and Simp...
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The compound interest on a certain sum for 2 years is Rs. 756 and Simp...
Given:
Compound Interest (CI) for 2 years = Rs. 756
Simple Interest (SI) for 2 years = Rs. 720
Simple Interest (SI) for n years = Rs. 900 (where n is the rate percent per annum)
To find: Rate percent
Formula:
Compound Interest formula: CI = P[(1 + r/100)^n - 1]
Simple Interest formula: SI = Pnr/100
Approach:
1. Using the given data, calculate the rate percent for the Simple Interest for 2 years.
2. Using the rate percent calculated in step 1, calculate the Principal amount.
3. Using the Principal amount and the given Compound Interest for 2 years, calculate the rate percent for the Compound Interest.
4. Using the given Simple Interest for n years and Principal amount, calculate the rate percent.
Calculation:
1. Rate percent for SI for 2 years = (100*SI)/(P*n) = (100*720)/(P*2) = 36/P
2. Using the rate percent calculated in step 1, calculate the Principal amount:
36/P = r
P = (100*SI)/(r*n) = (100*720)/(r*2)
3. Using the Principal amount and the given Compound Interest for 2 years, calculate the rate percent for the Compound Interest:
756 = P[(1 + r/100)^2 - 1]
(1 + r/100)^2 = 1 + 756/P
(1 + r/100) = sqrt(1 + 756/P)
r = 100*(sqrt(1 + 756/P) - 1)
4. Using the given Simple Interest for n years and Principal amount, calculate the rate percent:
900 = Pnr/100
n = (100*900)/(P*r)
Substituting the value of P from step 2 and r from step 3 in step 4:
n = (100*900)/(720*(sqrt(1 + 756/((100*720)/(36/P)))) = 5
Therefore, the rate percent per annum is 5% (Option C).
Note: The calculation can be simplified using approximation methods.
Compound Interest (CI) for 2 years = Rs. 756
Simple Interest (SI) for 2 years = Rs. 720
Simple Interest (SI) for n years = Rs. 900 (where n is the rate percent per annum)
To find: Rate percent
Formula:
Compound Interest formula: CI = P[(1 + r/100)^n - 1]
Simple Interest formula: SI = Pnr/100
Approach:
1. Using the given data, calculate the rate percent for the Simple Interest for 2 years.
2. Using the rate percent calculated in step 1, calculate the Principal amount.
3. Using the Principal amount and the given Compound Interest for 2 years, calculate the rate percent for the Compound Interest.
4. Using the given Simple Interest for n years and Principal amount, calculate the rate percent.
Calculation:
1. Rate percent for SI for 2 years = (100*SI)/(P*n) = (100*720)/(P*2) = 36/P
2. Using the rate percent calculated in step 1, calculate the Principal amount:
36/P = r
P = (100*SI)/(r*n) = (100*720)/(r*2)
3. Using the Principal amount and the given Compound Interest for 2 years, calculate the rate percent for the Compound Interest:
756 = P[(1 + r/100)^2 - 1]
(1 + r/100)^2 = 1 + 756/P
(1 + r/100) = sqrt(1 + 756/P)
r = 100*(sqrt(1 + 756/P) - 1)
4. Using the given Simple Interest for n years and Principal amount, calculate the rate percent:
900 = Pnr/100
n = (100*900)/(P*r)
Substituting the value of P from step 2 and r from step 3 in step 4:
n = (100*900)/(720*(sqrt(1 + 756/((100*720)/(36/P)))) = 5
Therefore, the rate percent per annum is 5% (Option C).
Note: The calculation can be simplified using approximation methods.
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