A sum of Rs 18,000 becomes Rs 21,780 after 2 years on compound interest compounded annually. What will be the compound interest (in Rs) on the same sum for the same period if the rate of interest increases by 5%?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 5805
Sum = Rs. 18000
Amount = Rs. 21780
Time = 2 years
A = P(1 + r/100)t
I = P(1 + r/100)t - P
A = amount, P = principal, r = rate, t = time, I = interest
Let the rate of interest be r.
21780 = 18000(1 + r/100)2
21780/18000 = (1 + r/100)2
1089/900 = (1 + r/100)2
(33/30)2 = (1 + r/100)2
33/30 = (1 + r/100)
33/30 = [(100 + r)/100]
3300 = 3000 + 30r
30r = 300
r = 300/30
r = 10%
New rate = 15%
I = 18000(1 + 15/100)2 - 18000
I = 18000(1 + 3/20)2 - 18000
I = 18000[(20 + 3)/20]2 - 18000
I = 18000[(23/20]2 - 18000
I = 18000 × (529/400) - 18000
I = 23805 - 18000
I = 5805
Interest for the new rate = Rs. 5805