The compound interest on a sum of Tk. 625 in 2 years is Tk. 51. Find the rate of interest.

Question: The compound interest on a sum of Tk. 625 in 2 years is Tk. 51. Find the rate of interest.

Solution:
We know that A = CI + P
A = 51 + 625 = 676

Now going by the formula:
A = P[1+(R/100)]ⁿ
⇒ 676 = 625[1 + (R/100)]²
⇒ 676/625 = [1 + (R/100)]²
We can see that 676 is the square of 26 and 625 is the square of 25
Therefore,
⇒ (26/25)² = [1 + (R/100)]²
⇒ 26/25 = [1 + (R/100)]
⇒ 26/25 - 1 = R/100
⇒ 1/25 = R/100
⇒ R = 100/25
∴ R = 4