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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 :
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- 25%
- 30%
- 45%
- 50%
Correct Option: D
Suppose P = ₹ 100 and amount A = ₹ 225
Time = 2 years , Rate = r%
A = P | ![]() | 1 + | ![]() | t | |
100 |
⇒ 225 = 100 | ![]() | 1 + | ![]() | 2 | |
100 |
⇒ | = | ![]() | 1 + | ![]() | 2 | ||
100 | 100 |
⇒ 1 + | = | ||
100 | 10 |
⇒ | = | ||
100 | 10 |
⇒ 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%