Question

The compound interest on a certain sum for two years is Rs. 618 whereas the simple interest on the same sum at the same rate for two years is Rs. 600. The ratio of interest per annum is

1.  6%

2.  3%

3.  9%

4.  18%

Answer 1

(i)

We know that Compound interest = P(1 + r/100)^n - P

⇒ P[(1 + r/100)^n - 1].

Given that compound interest on a sum for 2 years is 618.

⇒ P[(1 + r/100)^2 - 1] = 618.    ----- (1)

(ii)

We know that SI = PRT/100.

Simple interest on the same sum at the same rate for two years is 600.

⇒ (PR * 2/100) = 600

⇒ PR/50 = 600

⇒ PR = 30000.    ----- (2)

On solving  (1), we get

⇒ P[(1 + r^2/10000 + 2r/100) - 1] = 618

⇒ P[r^2/10000 + 2r/100] = 618

⇒ (Pr^2/10000 + 2pr/100) = 618

⇒ (PR * R/10000 + 2PR/100) = 618

⇒ (30000 * R/10000 + 2*30000/100) = 618 [∴ From (2)]

⇒ (3R + 600) = 618

⇒ 3R = 18

⇒ R = 6.

Therefore, rate of interest = 6%. - Option(A).

Hope it helps!