Compound Interest
- A sum of ₹ 12,000, deposited at compound interest becomes double after 5 years. How much will it be after 20 years ?
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Here , Principal ( P ) = ₹ 12,000 , Amount = 2P = ₹ 24,000 , Time = 5 years , Rate = R%
A = P 
1 + R 
T 100 ⇒ 24000 = 12000 1 + R 5 100 ⇒ 2 = 1 + R 5 100 Now, we have 24 = 1 + R 20 100
∴ The sum amounts to 16 times of principal i.e. ₹ 192000 after 20 years.
Second Method to solve this question :
Here, p = 2, n1 = 5
q = ?, n2 = 20
∴ p1/n1 = q1/n
Correct Option: D
Here , Principal ( P ) = ₹ 12,000 , Amount = 2P = ₹ 24,000 , Time = 5 years , Rate = R%
A = P 1 + R T 100 ⇒ 24000 = 12000 1 + R 5 100 ⇒ 2 = 1 + R 5 100 Now, we have 24 = 1 + R 20 100
∴ The sum amounts to 16 times of principal i.e. ₹ 192000 after 20 years.
Second Method to solve this question :
Here, p = 2, n1 = 5
q = ?, n2 = 20
∴ p1/n1 = q1/n
21/5 = y1/20
⇒ y = (21/5)20
q = 24
q = 16 times
∴ Sum = 16 × 12000 = ₹ 1,92,000
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compounded annually, then the rate of interest per annum isIf the amount is 3 3 times the sum after 3 years at compound interest 8
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Given that , Time = 3 years , Rate = R%
Let Principal be P .A = P 1 + R T 100
From the question ,⇒ 27 P = P 
1 + R 3 8 100 ⇒ 3 3 = 1 + R 3 2 100 ⇒ 1 + R = 3 100 2 ⇒ R = 3 − 1 = 1 100 2 2 ⇒ R = 1 × 100 2
∴ R = 50%
Using the given formula :Here , n = 27 , t = 3 years 8
R% = (n1/n − 1) × 100%R% = 
27 1/3 − 1 
× 100 8
Correct Option: B
Given that , Time = 3 years , Rate = R%
Let Principal be P .A = P 1 + R T 100
From the question ,⇒ 27 P = P 1 + R 3 8 100 ⇒ 3 3 = 1 + R 3 2 100 ⇒ 1 + R = 3 100 2 ⇒ R = 3 − 1 = 1 100 2 2 ⇒ R = 1 × 100 2
∴ R = 50%
Using the given formula :Here , n = 27 , t = 3 years 8
R% = (n1/n − 1) × 100%R% = 27 1/3 − 1 × 100 8 R% = 3 − 1 × 100 2 R% = 1 × 100 = 50% 2
- A sum of money placed at compound interest doubles itself in 5 years. In how many years, it would amount to eight times of itself at the same rate of interest ?
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Let the Principal be P and rate of interest be r%.
∴ 2 P = P 1 + r 2 100 ⇒ 2 = 1 + r 5 ...(i) 100
On cubing both sides, we get8 = 1 + r 15 100
On multiplying by P both sides ,8P = P 1 + r 15 100
Correct Option: B
Let the Principal be P and rate of interest be r%.
∴ 2 P = P 1 + r 2 100 ⇒ 2 = 1 + r 5 ...(i) 100
On cubing both sides, we get8 = 1 + r 15 100
On multiplying by P both sides ,8P = P 1 + r 15 100
∴ The sum will be 8 times in 15 years. i.e., Time = 15 years
We can find required answer with the help of given formula :
Here, m = 2, t = 5 years
It becomes 8 times = 23 times
in t × n = 5 × 3 = 15 years
- A sum of money invested at compound interest doubles itself in 6 years. At the same rate of interest it will amount to eight times of itself in :
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Here , Time = 6 years , Rate = r%
Let the sum be P. Then,
From the question ,2P = P 1 + r 6 100 ⇒ 2 = 1 + r 6 100
Cubing on both sides, we get8 = 
1 + r 6 
3 100 ⇒ 8 = 1 + r 18 100
Multiplying by P both sides ,⇒ 8P = P 1 + r 18 100
∴ The sum will be 8 times in 18 years. i.e., Time = 18 years
Correct Option: C
Here , Time = 6 years , Rate = r%
Let the sum be P. Then,
From the question ,2P = P 1 + r 6 100 ⇒ 2 = 1 + r 6 100
Cubing on both sides, we get8 = 1 + r 6 3 100 ⇒ 8 = 1 + r 18 100
Multiplying by P both sides ,⇒ 8P = P 1 + r 18 100
∴ The sum will be 8 times in 18 years. i.e., Time = 18 years
Second Method to find required answer :
Here, m = 2, t = 6 years
It will becomes 8 times of itself = 23 times of itself in t × n years = 6 × 3 = 18 years
- A sum of money becomes eight times of itself in 3 years at compound interest. The rate of interest per annum is
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Let the principal be P and the rate of compound interest be r% per annum. Then,
According to question ,8P = P 1 + r 3 100 ⇒ 8 = 1 + r 3 ⇒ 23 = 1 + r 3 100 100 ⇒ 2 = 1 + r 100 ⇒ r = 1 ⇒ r = 100% 100
We can find required answer with the help of given formula :
Here, n = 8, t = 3 years.
R% = (n1/t − 1) × 100%
Correct Option: A
Let the principal be P and the rate of compound interest be r% per annum. Then,
According to question ,8P = P 1 + r 3 100 ⇒ 8 = 1 + r 3 ⇒ 23 = 1 + r 3 100 100 ⇒ 2 = 1 + r 100 ⇒ r = 1 ⇒ r = 100% 100
We can find required answer with the help of given formula :
Here, n = 8, t = 3 years.
R% = (n1/t − 1) × 100%
R% = [(8)1/3 − 1] × 100%
R% = [(23)1/3 − 1] × 100%
∴ R% = 100%
