## Compound Interest

#### Compound Interest

1. The difference between the compound interest and the simple interest on a certain sum at 5% per annum for 2 years is Rs. 1.50. The sum is ?

1. Let the sum be Rs . 100 then
S.I. = Rs.(100 x 5 x 2/100)= Rs. 10
C.I = Rs. [{100 x (1 + 5/100)2} - 100] = Rs. 41/4

∴ Difference between C.I and S.I = Rs. (41/4 - 10) = Re. 0.25
⇒ 0.25 : 150 : : 100 : P
∴ P = (1.50 x 100) / 0.25 = Rs. 600

##### Correct Option: A

Let the sum be Rs . 100 then
S.I. = Rs.(100 x 5 x 2/100)= Rs. 10
C.I = Rs. [{100 x (1 + 5/100)2} - 100] = Rs. 41/4

∴ Difference between C.I and S.I = Rs. (41/4 - 10) = Re. 0.25
⇒ 0.25 : 150 : : 100 : P
∴ P = (1.50 x 100) / 0.25 = Rs. 600

1. If the compound interest on a certain sum for 2 years at 12.5% per annum is 170, the simple interest is ?

1. Let the principle is P
so compound interest = p x ( 1 + (12.5/100))sup>2 - p = 170
⇒ p x (112.5/100) x (112.5/100) - p = 170
⇒ P [ 12656.25 - 10000 ] = 170 x 10000
∴ p = (170 x 10000) / 2656.25

Simple interest SI = (P x T x R )/100
= [{(170 x 10000) / 2656.25} x 2 x 12.5] / 100
= 160

##### Correct Option: C

Let the principle is P
so compound interest = p x ( 1 + (12.5/100))sup>2 - p = 170
⇒ p x (112.5/100) x (112.5/100) - p = 170
⇒ P [ 12656.25 - 10000 ] = 170 x 10000
∴ p = (170 x 10000) / 2656.25

Simple interest SI = (P x T x R )/100
= [{(170 x 10000) / 2656.25} x 2 x 12.5] / 100
= 160

1. A sum amounts to Rs. 1352 in 2 years at 4% compound interest.The sum is ?

1. Let the sum be P.
Then, 1352 = P(1 +4/100)2

##### Correct Option: B

Let the sum be P.
Then, 1352 = P(1 +4/100)2
⇒ 1352 = P x 26/25 x 26/25
⇒ P = (1352 x 25 x 25) / (26 x 26) = 1250
∴ Principal = Rs. 1250

1. Rs. 800 at 5% per annum compound interest will amount to Rs. 882 in ?

1. Let time be t years
∵ 882 = 800( 1 +5/1000)t
⇒ 882/800 = (21/20)t

##### Correct Option: B

Let time be t years
∵ 882 = 800( 1 +5/1000)t
⇒ 882/800 = (21/20)t
⇒ (21/20)2 = (21/20)t
⇒ t =2
∴ Time = 2years

1. The compound interest on Rs. 2800 for 11/2 years at 10% per annum is ?

1. ∵ Final Amount = Rs.[2800 x (1 + 10/100) x (1 +5/100)]
= Rs. [ 2800 x 11/10 x 21/20 ]
= Rs. 3234

##### Correct Option: C

∵ Final Amount = Rs.[2800 x (1 + 10/100) x (1 +5/100)]
= Rs. [ 2800 x 11/10 x 21/20 ]
= Rs. 3234

∴ Required C.I. = Rs.(3234 - 2800) = Rs .434