An amount of Tk 10000 becomes Tk 11025 in 1 year if the interest is compounded half-yearly. What is the rate of compound interest per annum?

Question: An amount of Tk 10000 becomes Tk 11025 in 1 year if the interest is compounded half-yearly. What is the rate of compound interest per annum?

Solution:
Let the compound interest be r%

ATQ,
10000 × {1 + (r/2)}² = 11025
⇒ {(2 + r)/2}² = 11025/10000
⇒ (2 + r)/2 = 105/100 [applying square root]
⇒ 2 + r = 210/100
⇒ 200 + 100r = 210
⇒ 100r = 10
⇒ r = 10/100
⇒ r = (10/100%) × 100
⇒ r = 10%