Compound Interest
- A sum of ₹ 1682 is to be divided between A and B who are respectively 20 years and 22 years old. They invest their shares at 5% per annum, compounded annually. At the age of 25 years both receive equal amounts. Find the share of each.
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Given in question , Rate = 5% per annum
For A, time = 5 years
For B, time = 3 years
r = 5% per annum
According to question ,A 
1 + 5 
5 = B 1 + 5 3 100 100 B = 1 + 5 2 A 100 B = 441 A 400
Sum of ratio = 400 + 441 = 841
As given, sum = A + B = ₹ 1682
Correct Option: D
Given in question , Rate = 5% per annum
For A, time = 5 years
For B, time = 3 years
r = 5% per annum
According to question ,A 1 + 5 5 = B 1 + 5 3 100 100 B = 1 + 5 2 A 100 B = 441 A 400
Sum of ratio = 400 + 441 = 841
As given, sum = A + B = ₹ 1682So, A = 400 ×1682 = ₹ 800 841 and B = 441 ×1682 = ₹ 882 841
- Divide ₹ 10230 into two parts such that the first part after 10 years is equal to the second part after 7 years, compound interest being 20% per annum compounded yearly.
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Let the first part be p and the second part q.
The first part after 10 years = p 
1 + 20 
10 100 The second part after 7 years = q 1 + 20 7 100
As given in the problem these two amounts are equal.
So,q 1 + 20 7 = p 1 + 20 10 100 100 ⇒ q = 1 + 20 3 p 100 ⇒ q = 216 p 125
and we have p + q = ₹ 10230
Correct Option: C
Let the first part be p and the second part q.
The first part after 10 years = p 1 + 20 10 100 The second part after 7 years = q 1 + 20 7 100
As given in the problem these two amounts are equal.
So,q 1 + 20 7 = p 1 + 20 10 100 100 ⇒ q = 1 + 20 3 p 100 ⇒ q = 216 p 125
and we have p + q = ₹ 10230
Using the ratio formulaq = 216 ×10230 = ₹ 6480 216 + 125 p = 125 ×10230 = ₹ 3750 216 + 125
- A sum amounts to ₹ 9680 in 2 years and to ₹ 10648 in 3 years compounded annually. Find the principal and the rate of interest per annum.
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Let Principal = P , Rate = r% p.a.
Here , A1 = ₹ 9680 , t1 = 2 years , A2 = ₹ 10648 , t2 = 3 years
Interest on ₹ 9680 for 1 year = 10648 – 9680 = ₹ 968∴ r = 968 × 100 = 10% 9680
Using the given formula,A = P 1 + r t 100
we get ,9680 = P 1 + 10 2 = P 11 2 100 10
Correct Option: B
Let Principal = P , Rate = r% p.a.
Here , A1 = ₹ 9680 , t1 = 2 years , A2 = ₹ 10648 , t2 = 3 years
Interest on ₹ 9680 for 1 year = 10648 – 9680 = ₹ 968∴ r = 968 × 100 = 10% 9680
Using the given formula,A = P 1 + r t 100
we get ,9680 = P 1 + 10 2 = P 11 2 100 10 ⇒ P = 9680 × 10 × 10 = 8000 11 11
∴ Principal = ₹ 8000.
- If the difference between CI and SI on a certain sum at r% per annum for 3 years is Rs x, find the expression for the principal sum. If the difference between CI and SI on a certain sum at 4% for 3 years is Rs. 608. Find the sum.
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Let the sum be ₹ P and rate = r%
Here , t = 3 yearsSI = Pr × 3 = 3 Pr 100 100 C.I. = P 
1 + r 3 − 1 100 CI = P 1 + r3 + 3r2 + 3r − 1 1003 1002 100 CI = P r3 + 3r2 + 3r 1003 1002 100 ⇒ CI – SI ( D ) = P r3 + 3r2 + 3r − 3Pr 1003 1002 100 100 D = P r3 + 3r2 1003 1002
Correct Option: A
Let the sum be ₹ P and rate = r%
Here , t = 3 yearsSI = Pr × 3 = 3 Pr 100 100 C.I. = P 1 + r 3 − 1 100 CI = P 1 + r3 + 3r2 + 3r − 1 1003 1002 100 CI = P r3 + 3r2 + 3r 1003 1002 100 ⇒ CI – SI ( D ) = P r3 + 3r2 + 3r − 3Pr 1003 1002 100 100 D = P r3 + 3r2 1003 1002 D = P r2 [r + 300] 1003 P = D (100)3 r2(r + 300)
Given Here, D = ₹ 608 and r = 4% per annumP = 608 × 100 × 100 × 100 4 × 4 × (4 + 300)
P = Rs. 1,25,000.
- A certain sum amounts to ₹ 5,832 in 2 years at 8% per annum compound interest, the sum is
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Here , P = ? , A = ₹ 5,832 , R = 8%, T = 2 years
Using the given formula ,A = P 1 + R T 100 5832 = P 1 + 8 2 100 ⇒ 5832 = P 1 + 2 2 25
Correct Option: A
Here , P = ? , A = ₹ 5,832 , R = 8%, T = 2 years
Using the given formula ,A = P 1 + R T 100 5832 = P 1 + 8 2 100 ⇒ 5832 = P 1 + 2 2 25 ⇒ 5832 = P × 27 × 27 25 25 ⇒ P = 5832 × 25 × 25 = ₹ 5000 27 × 27
