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  1. If the amount is 2.25 times of the sum after 2 years at compound interest (compound annually), the rate of interest per annum is :
    1. 25%
    2. 30%
    3. 45%
    4. 50%
Correct Option: D

Suppose P = ₹ 100 and amount A = ₹ 225
Time = 2 years , Rate = r%

A = P1 +
r
t
100

⇒ 225 = 1001 +
r
2
100

225
= 1 +
r
2
100100

⇒ 1 +
r
=
15
10010

100 + r
=
15
10010

⇒ 100 + r = 150 ⇒ r = 150 - 100
⇒ r = 50%
We can find required answer with the help of given formula :
Here, n = 2.25 , t = 2 years
R% = (n1/t − 1) × 100%
R% = [(2.25)1/2 − 1] × 100%
R% = [1.5 − 1] × 100%
R% = 0.5 × 100% = 50%



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