## Compound Interest

#### Compound Interest

1. A sum becomes ₹ 1,352 in 2 years at 4% per annum compound interest. The sum is

1. Let the sum be ₹ p.
Here , A = ₹ 1352 , r = 4% , n = 2 years
Using the given formula ,

 A = P 1 + r n 100

 ∴  1352 = p 1 + 4 2 100

 ⇒  1352 = p 1 + 1 2 25

##### Correct Option: D

Let the sum be ₹ p.
Here , A = ₹ 1352 , r = 4% , n = 2 years
Using the given formula ,

 A = P 1 + r n 100

 ∴  1352 = p 1 + 4 2 100

 ⇒  1352 = p 1 + 1 2 25

 ⇒  1352 = p 26 2 25

 ⇒  p = 1352 × 25 × 25 = ₹ 1250 26 × 26

1. At what rate percent per annum will ₹ 2304 amount to ₹ 2500 in 2 years at compound interest ?

1. Let the rate percent per annum be r.
Given that , P = ₹ 2304 , A = ₹ 2500 , n = 2 years
Using the given formula ,

 A = P 1 + r n 100

 2500 = 2304 1 + r 2 100

 ⇒ 1 + r 2 = 2500 = 50 2 100 2304 48

 ⇒  1 + r = 50 = 25 100 48 24

 ⇒ r = 25 − 1 = 1 100 24 24

##### Correct Option: C

Let the rate percent per annum be r.
Given that , P = ₹ 2304 , A = ₹ 2500 , n = 2 years
Using the given formula ,

 A = P 1 + r n 100

 2500 = 2304 1 + r 2 100

 ⇒ 1 + r 2 = 2500 = 50 2 100 2304 48

 ⇒  1 + r = 50 = 25 100 48 24

 ⇒ r = 25 − 1 = 1 100 24 24

 ⇒  r = 100 = 25 = 4 1 % 24 6 6

1. A sum of money on compound interest amounts to ₹ 10648 in 3 years and ₹ 9680 in 2 years. The rate of interest per annum is :

1. Let the sum be ₹ P and rate of interest be R% per annum.
Here , A1 = ₹ 10648 , A2 = ₹ 9680
and t1 = 3 years , t2 = 2 years
Using the given formula ,

 A = P 1 + R n 100

Then,
 P 1 + R 2 = 9680    ...(i) 100

 P 1 + R 3 = 10648    ...(ii) 100

On dividing equation (ii) by (i)
 1 + R = 10648 100 9680

 ⇒ R = 10648 − 1 100 9680

 = 10648 − 9680 9680

##### Correct Option: B

Let the sum be ₹ P and rate of interest be R% per annum.
Here , A1 = ₹ 10648 , A2 = ₹ 9680
and t1 = 3 years , t2 = 2 years
Using the given formula ,

 A = P 1 + R n 100

Then,
 P 1 + R 2 = 9680    ...(i) 100

 P 1 + R 3 = 10648    ...(ii) 100

On dividing equation (ii) by (i)
 1 + R = 10648 100 9680

 ⇒ R = 10648 − 1 100 9680

 = 10648 − 9680 9680

 ⇒ R = 968 = 1 100 9680 10

 ⇒  R = 1 × 100 = 10% 10

1. The principal, which will amount to ₹ 270.40 in 2 years at the rate of 4% per annum compound interest, is

1. Let the principal be ₹ P.
Here , A = ₹ 270.40 , r = 4%, n = 2 years
Using the given formula ,

 A = P 1 + r n 100

 ∴  270.40 = P 1 + 4 2 100

⇒  270.40 = P (1 + 0.04)2

##### Correct Option: C

Let the principal be ₹ P.
Here , A = ₹ 270.40 , r = 4%, n = 2 years
Using the given formula ,

 A = P 1 + r n 100

 ∴  270.40 = P 1 + 4 2 100

⇒  270.40 = P (1 + 0.04)2
 ⇒  P = 270.40 = ₹ 250 1.04 × 1.04

1. In what time will ₹ 1000 becomes ₹ 1331 at 10% per annum compounded annually ?

1. Here , P = ₹ 1000, P1 = ₹ 1331 , r = 10%
Let the required time be n years. Then,
Using the given formula ,

 ∴  P1 = P 1 + r n 100

 1331 = 1000 1 + 10 n 100

 ⇒ 1331 = 10 + 1 n 1000 10

##### Correct Option: A

Here , P = ₹ 1000, P1 = ₹ 1331 , r = 10%
Let the required time be n years. Then,
Using the given formula ,

 ∴  P1 = P 1 + r n 100

 1331 = 1000 1 + 10 n 100

 ⇒ 1331 = 10 + 1 n 1000 10

 ⇒ 11 n = 11 3 10 10

Equating on both sides , we get
⇒  n = 3