Compound Interest
- If the difference between simple and compound interest on some principal amount at 20% per annum for three years is ₹ 48, then the principal amount is:
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Given that , Difference ( D ) = ₹ 48 , r = 20%
Using the given formula ,For three years , P = D × 1003 r2(r + 300)
Correct Option: B
Given that , Difference ( D ) = ₹ 48 , r = 20%
Using the given formula ,For three years , P = D × 1003 r2(r + 300) P = 48 × 1003 = Rs. 375 400(20 + 300)
- At what rate per annum will ₹ 32000 yield a compound interest of ₹ 5044 in 9 months interest being compounded quarterly ?
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Here , Compound interest ( CI ) = ₹ 5044 ,Principal ( P ) = ₹ 32000 , Time = 9 months = ( 9 / 12 ) year = ( 3 / 4 ) years
Let the rate of CI be R percent per annum.∴ CI = P 
1 + R 
T − 1 
100
∵ Interest is compounded quarterly⇒ 5044 = 32000 1 + R 3 − 1 400 ⇒ 5044 = 
1 + R 3 − 1 32000 400 ⇒ 1 + R 3 − 1 = 1261 400 8000 ⇒ 1 + R 3 = 1 + 1261 400 8000 ⇒ 1 + R 3 = 9261 = 21 3 400 8000 20
Correct Option: A
Here , Compound interest ( CI ) = ₹ 5044 ,Principal ( P ) = ₹ 32000 , Time = 9 months = ( 9 / 12 ) year = ( 3 / 4 ) years
Let the rate of CI be R percent per annum.∴ CI = P 1 + R T − 1 100
∵ Interest is compounded quarterly⇒ 5044 = 32000 1 + R 3 − 1 400 ⇒ 5044 = 1 + R 3 − 1 32000 400 ⇒ 1 + R 3 − 1 = 1261 400 8000 ⇒ 1 + R 3 = 1 + 1261 400 8000 ⇒ 1 + R 3 = 9261 = 21 3 400 8000 20 ⇒ 1 + R = 21 ⇒ R = 21 − 1 = 1 400 20 400 20 20 ⇒ R = 400 = 20 % per annum 20
- B borrows ₹ 5,000 from A at 6% p.a. simple interest and lends it to C at compound interest of 10% p.a. If B collects the money back from C after 2 years and repays A, the profit made by B in the transaction is
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Given that , Principal = ₹ 5,000 , Time = 2 years , Rate = 6% p.a
Interest got by A = Principal × Time × Rate 100 Interest got by A = 5000 × 2 × 6 = Rs. 600 100
Now , Time = 2 years , Rate = 10% p.aC.I. received by B = P 1 + R T − 1 100 C.I. received by B = 5000 1 + 10 2 − 1 100 C.I. received by B = 5000 11 2 − 1 10
Correct Option: C
Given that , Principal = ₹ 5,000 , Time = 2 years , Rate = 6% p.a
Interest got by A = Principal × Time × Rate 100 Interest got by A = 5000 × 2 × 6 = Rs. 600 100
Now , Time = 2 years , Rate = 10% p.aC.I. received by B = P 1 + R T − 1 100 C.I. received by B = 5000 1 + 10 2 − 1 100 C.I. received by B = 5000 11 2 − 1 10 C.I. received by B = 5000 121 − 1 100 C.I. received by B = 5000 × 21 = Rs. 1050 100
B’s profit = C.I. received by B - Interest got by A
∴ B’s profit = Rs. (1050 – 600) = Rs. 450
- Rs. 260200 is divided between Ram and Shyam so that the amount that Ram receives in 4 years is the same as that Shyam receives in 6 years. If the interest is compounded annually at the rate of 4% per annum then Ram’s share is
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Let Ram’s share be Rs. y.
∴ Shyam’s share = Rs. (260200 – y)A = P 1 + R T 100
According to question ,⇒ y 1 + R 4 = (260200 – y) 1 + R 6 100 100 ⇒ y = (260200 – y) 1 + 4 2 100 ⇒ y = (260200 – y) 1 + 1 2 25 ⇒ y = (260200 – y) 26 2 25 ⇒ y = (260200 – y) 676 625 ⇒ 625y + y = 260200 676 ⇒ 625y + 676y = 260200 676
Correct Option: B
Let Ram’s share be Rs. y.
∴ Shyam’s share = Rs. (260200 – y)A = P 1 + R T 100
According to question ,⇒ y 1 + R 4 = (260200 – y) 1 + R 6 100 100 ⇒ y = (260200 – y) 1 + 4 2 100 ⇒ y = (260200 – y) 1 + 1 2 25 ⇒ y = (260200 – y) 26 2 25 ⇒ y = (260200 – y) 676 625 ⇒ 625y + y = 260200 676 ⇒ 625y + 676y = 260200 676 ⇒ 1301y = 260200 676 ⇒ y = 260200 × 676 = Rs. 135200 1301
- A man borrowed some money and agreed to pay-off by paying Rs. 3150 at the end of the 1st year and Rs. 4410 at the end of the 2nd year. If the rate of compound interest is 5% per annum, then the sum is
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As per the given in question , y1 = Rs. 3150 , y2 = Rs. 4410 , R = 5%
P = y1 + y2 1 + R 1 + R 
2 10 10 
Correct Option: C
As per the given in question , y1 = Rs. 3150 , y2 = Rs. 4410 , R = 5%
P = x1 + x2 1 + R 1 + R 2 10 10 P = Rs. 3150 × 20 + 4410 × 400 21 441
P = Rs. (3000 + 4000)
P = Rs. 7000
