Compound Interest
- On a certain principal if the simple interest for two years is Rs. 1400 and compound interest for the two years is Rs. 1449, what is the rate of interest?
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Given that , S.I. = Rs. 1400 , C.I = Rs. 1449
Let the principal be Rs. P and rate of interest be R% per annum.∴ S.I.= Principal × Time × Rate 100 ⇒ 1400 = PR × 2 100
⇒ PR = 1400 × 50 = 70000 ..... (i)
Again, for 2 years,C.I. – S.I. = PR2 10000 ⇒ 1449 – 1400 = PR2 10000
Correct Option: A
Given that , S.I. = Rs. 1400 , C.I = Rs. 1449
Let the principal be Rs. P and rate of interest be R% per annum.∴ S.I.= Principal × Time × Rate 100 ⇒ 1400 = PR × 2 100
⇒ PR = 1400 × 50 = 70000 ..... (i)
Again, for 2 years,C.I. – S.I. = PR2 10000 ⇒ 1449 – 1400 = PR2 10000 ⇒ 49 = PR × R 10000 ⇒ 49 = 70000 × R 10000
[From equation (i)]
⇒ 7R = 49⇒ R = 49 = 7% per annum 7
- The amount of Rs. 10,000 after 2 years, compounded annually with the rate of interest being 10% per annum during the first year and 12% per annum during the second year, would be (in rupees)
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Here , Principal = Rs. 10000 , R1 = 10% , R2 = 12%
A = P 
1 + R1 
1 + R2 100 100 A = 10000 1 + 10 1 + 12 100 100
Correct Option: C
Here , Principal = Rs. 10000 , R1 = 10% , R2 = 12%
A = P 1 + R1 1 + R2 100 100 A = 10000 1 + 10 1 + 12 100 100 A = 10000 × 110 × 112 100 100
∴ A = Rs. 12320
- If the difference between CI and SI on a certain sum at r% per annum for 2 years is ₹ x, find the expression for principal sum. If the difference between CI and SI on a certain sum at 4% per annum for 2 years is ₹ 25, find the sum.
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Let the sum be ₹ P
SI = Pr × 2 = 2 Pr 100 100 C.I. = P 
1 + r 2 − 1 
100 = P 1 + r2 + 2r − 1 (100)2 100 CI = P r2 + 2r 1002 100 CI – SI = P r2 + 2r − 2Pr 1002 100 100
Let, CI – SI = yy = Pr2 ⇒ P = y 100 2 1002 r
Here, y = ₹ 25 , r = 4% per annum
Correct Option: D
Let the sum be ₹ P
SI = Pr × 2 = 2 Pr 100 100 C.I. = P 1 + r 2 − 1 100 = P 1 + r2 + 2r − 1 (100)2 100 CI = P r2 + 2r 1002 100 CI – SI = P r2 + 2r − 2Pr 1002 100 100
Let, CI – SI = yy = Pr2 ⇒ P = y 100 2 1002 r
Here, y = ₹ 25 , r = 4% per annumP = 25 100 2 4
P = 25× 625
P = ₹ 15625.
- The sum of money which when given on compound interest at 18% per annum would fetch Rs. 960 more when the interest is payable half yearly than when it was payable annually for 2 years is :
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As per the given in question ,
When the interest is payable half yearly,
Rate = 9% per half annum , Time = 4 half years
Let the principal be Rs. P.∴ C.I. = P 1 + R T − 1 100 C.I. = P 1 + 9 4 − 1 100
C.I. = P[(1.09)4 − 1]
C.I. = P [1.4116 – 1] = Rs. 0.4116 P
According to the question,= P 1 + 18 2 − 1 100
= P[(1.18)2 − 1]
= P (1.3924 – 1) = Rs. 0.3924 P
Correct Option: D
As per the given in question ,
When the interest is payable half yearly,
Rate = 9% per half annum , Time = 4 half years
Let the principal be Rs. P.∴ C.I. = P 1 + R T − 1 100 C.I. = P 1 + 9 4 − 1 100
C.I. = P[(1.09)4 − 1]
C.I. = P [1.4116 – 1] = Rs. 0.4116 P
According to the question,= P 1 + 18 2 − 1 100
= P[(1.18)2 − 1]
= P (1.3924 – 1) = Rs. 0.3924 P
According to the question,
0.4116P – 0.3924P = 960
⇒ 0.0192P = 960⇒ P = 960 0.0192 P = 960 × 10000 = Rs. 50000 192
- A sum of money placed at compound interest doubles itself in 5 years. It will amount to eight times of itself at the same rate of interest in
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Here , Time = 5 years
Let principal be P and Amount = 2P
Using the given formula ,A = P 1 + R n 100 ⇒ 2P = P 1 + R 5 100
On cubing both sides,23 = 1 + R 5 × 3 100 ⇒ 8 = 1 1 + R 15 100
∴ Required time = 15 years
Second Method to solve this question :
p = 2, n1 = 5, q = 8, n2 = ?
Here, p 1/n1 = q1/n2
Correct Option: D
Here , Time = 5 years
Let principal be P and Amount = 2P
Using the given formula ,A = P 1 + R n 100 ⇒ 2P = P 1 + R 5 100
On cubing both sides,23 = 1 + R 5 × 3 100 ⇒ 8 = 1 1 + R 15 100
∴ Required time = 15 years
Second Method to solve this question :
p = 2, n1 = 5, q = 8, n2 = ?
Here, p 1/n1 = q1/n2
(2)1/5 = (8)1/n2
21/5 = (2)3/n2⇒ 1 = 3 5 n2
∴ n2 = 15
