Compound Interest
- The compound interest on a certain sum of money for 2 years at 5% per annum is ₹ 410. The simple interest on the same sum at the same rate and for the same time is
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Here , Compound Interest ( CI ) = ₹ 410 , Rate ( R ) = 5% , Time = 2 years
Compound interest = P 
1 + R 
T − 1 
100 ⇒ 410 = P 1 + 5 2 − 1 100 ⇒ 410 = P 1 + 1 2 − 1 20 ⇒ 410 = P 21 2 − 1 20 ⇒ 410 = P 
441 − 1 400 ⇒ 410 = P 41 400 ⇒ P = 410 × 400 = ₹ 4000 41 ∴ S.I.= Principal × Time × Rate 100 S.I. = 4000 × 2 × 5 = ₹ 400 100
We can find required answer with the help of given formula :
Here, C.I. = Rs. 410 , R = 5% , S.I. = ?C.I.= S.I. 1 + R 200
Correct Option: A
Here , Compound Interest ( CI ) = ₹ 410 , Rate ( R ) = 5% , Time = 2 years
Compound interest = P 1 + R T − 1 100 ⇒ 410 = P 1 + 5 2 − 1 100 ⇒ 410 = P 1 + 1 2 − 1 20 ⇒ 410 = P 21 2 − 1 20 ⇒ 410 = P 441 − 1 400 ⇒ 410 = P 41 400 ⇒ P = 410 × 400 = ₹ 4000 41 ∴ S.I.= Principal × Time × Rate 100 S.I. = 4000 × 2 × 5 = ₹ 400 100
We can find required answer with the help of given formula :
Here, C.I. = Rs. 410 , R = 5% , S.I. = ?C.I.= S.I. 1 + R 200 410 = S.I. 1 + 5 200 410 = S.I. 205 200 S.I. =
410 × 200 = Rs.400 205
- The compound interest on a certain sum of money at a certain rate per annum for two years is ₹ 2,050, and the simple interest on the same amount of money at the same rate for 3 years is ₹ 3,000. Then the sum of money is
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Given in question , S.I. for 3 years = ₹ 3000
S.I. for 2 years = 3000 × 2 = ₹ 2000 3
∴ Difference = C.I. – S.I. = 2050 – 2000 = ₹ 50S.I. = PR × 3 100 ⇒ 3000 = PR × 3 100 ⇒ PR = 3000 × 100 = ₹ 100000 3
Correct Option: A
Given in question , S.I. for 3 years = ₹ 3000
S.I. for 2 years = 3000 × 2 = ₹ 2000 3
∴ Difference = C.I. – S.I. = 2050 – 2000 = ₹ 50S.I. = PR × 3 100 ⇒ 3000 = PR × 3 100 ⇒ PR = 3000 × 100 = ₹ 100000 3 ∴ Difference = P × R2 10000 ⇒ 50 = P × (100000)2 10000 × P2 ⇒ P = 1000000 = ₹ 20000 50
- A sum becomes ₹ 2,916 in 2 years at 8% per annum compound interest. The simple interest at 9% per annum for 3 years on the same amount will be
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Let principal be P.
Here , Amount ( A ) = ₹ 2,916 , Rate = 8% , Time = 2 years
Using the given formula ,A = P 1 + R T 100 ⇒ 2916 = P 1 + 8 2 100 ⇒ 2916 = P 27 2 25
Correct Option: B
Let principal be P.
Here , Amount ( A ) = ₹ 2,916 , Rate = 8% , Time = 2 years
Using the given formula ,A = P 1 + R T 100 ⇒ 2916 = P 1 + 8 2 100 ⇒ 2916 = P 27 2 25 ⇒ P = 2916 × 25 × 25 = ₹ 2500 27 × 27
Now, Time = 3 years , Rate = 9%∴ S.I.= P × R × T 100 S.I. = 2500 × 9 × 3 = ₹ 675 100
- If the compound interest on a certain sum for two years at 12% per annum is ₹ 2,544, the simple interest on it at the same rate for 2 years will be
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Given that , Compound Interest ( CI ) = ₹ 2,544 , Rate ( R ) = 12% , Time = 2 years
Using the given formula ,C.I. = P 1 + R T − 1 100 ⇒ 2544 = P 1 + 12 2 − 1 100 ⇒ 2544 = P 28 2 − 1 25 ⇒ 2544 = P 784 − 1 625 ⇒ 2544 = P 784 − 625 625 2544 = P × 159 625 ⇒ P = 2544 × 625 = ₹ 10000 159 ∴ S.I. = P × R × T 100 S.I. = 10000 × 2 × 12 = ₹ 2400 100
Second Method to solve this question :
Here, C.I. = Rs. 2544 , R = 12% , S.I. = ?C.I.= S.I. 1 + R 200
Correct Option: A
Given that , Compound Interest ( CI ) = ₹ 2,544 , Rate ( R ) = 12% , Time = 2 years
Using the given formula ,C.I. = P 1 + R T − 1 100 ⇒ 2544 = P 1 + 12 2 − 1 100 ⇒ 2544 = P 28 2 − 1 25 ⇒ 2544 = P 784 − 1 625 ⇒ 2544 = P 784 − 625 625 2544 = P × 159 625 ⇒ P = 2544 × 625 = ₹ 10000 159 ∴ S.I. = P × R × T 100 S.I. = 10000 × 2 × 12 = ₹ 2400 100
Second Method to solve this question :
Here, C.I. = Rs. 2544 , R = 12% , S.I. = ?C.I.= S.I. 1 + R 200 2544 = S.I. 1 + 12 200 2544 = S.I. 212 200 S.I. = 2544 × 200 = ₹ 2400 212
- There is 100% increase to an amount in 8 years, at simple interest. Find the compound interest of ₹ 8000 after 2 years at the same rate of interest.
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Let S.I. = ₹ 100, & Principal = ₹ 100
∴ Rate = S.I. × 100 Principal × Time Rate = 100 × 100 = 25 % 100 × 8 2
Given , Principal ( P ) = ₹ 8000 , Time = 2 years∴ C.I. = P 1 + r T − 1 100 C.I. = 8000 1 + 25 2 − 1 200
Correct Option: D
Let S.I. = ₹ 100, & Principal = ₹ 100
∴ Rate = S.I. × 100 Principal × Time Rate = 100 × 100 = 25 % 100 × 8 2
Given , Principal ( P ) = ₹ 8000 , Time = 2 years∴ C.I. = P 1 + r T − 1 100 C.I. = 8000 1 + 25 2 − 1 200 C.I. = 8000 81 − 1 64 C.I. = 8000 × 17 = ₹ 2125 64
