Question

A sum of money invested at compound interest, amounts to Rs.19360.00 in 2 years and to Rs. 23,425.60 in 4 years. Find the rate percent and the original sum of money.

Answer 1

Let the rate of interest be r% and principal be ₹ P.
So, for 2 years
C.I = P(1 + r/100)2
19360 = P(1 + r/100)2
So, P = 19360/[(1 + r/100)2] …….(i)
So, for 4 years
C.I = P(1 + r/100)4
23425.60 = P(1 + r/100)4
So, P = 23425.60/[(1 + r/100)4] …….(ii)
From (i) and (ii) , we get
19360/[(1 + r/100)2] = 23425.60/[(1 + r/100)4]
[(1 + r/100)4] = 1.21[(1 + r/100)2]
Let (1 + r/100)2 = x
So, x2 = 1.21(x)
        x2 – 1.21x = 0
       so, x = 1.21
    (1 + r/100)2 = 1.21
    (1 + r/100) = 1.1
           r/100 = 0.1
          so, r = 10%
p = 19360/[(1 + r/100)2] = 19360/[(1 + 10/100)2] = 19360/1.21 = 16,000
so, P = ₹ 16,000

Hope This Helps :)