Question

A sum invested in a scheme where the interest gets compounded quarterly grows to Rs 140000 and Rs
157304 respectively in 15 and 21 months respectively. What is the rate of interest per annum ? ​

Answer 1

Given info : A sum invested in a scheme where the interest gets compounded quarterly grows to Rs 140000 and Rs 157304 respectively in 15 and 21 months respectively.

To find : the rate of interest per annum is ...

solution : let the rate of interest is r % per annum.

a/c to question, sum is compounded quarterly.

so, r/4 % per quarter

case 1 : A = 140000 , t = 15 months = 15/3 = 5 quarters , rate = r/4

using formula, A = P(1 + r/100)^t

⇒140000 = P(1 + r/400)⁵ ...(1)

case 2 : A = 157304, t = 21 months = 21/3 = 7 quarters , rate = r/4

so, 157304 = P(1 + r/400)^7 ...(2)

dividing eq (2) by (1) we get,

157304/140000 = (1 + r/400)²

⇒1.1236 = (1 + r/400)²

⇒√(1.1236) = 1.06 = 1 + r/400

⇒r = 0.06 × 400 = 24 %

Therefore the rate of interest per annum is 24 % per annum.