A sum invested at a certain rate of interest per annum, compounded annually, amounts to ₹14,400 in 2 years and to ₹25,920 in 4 years. What is the sum invested?
Show answer & explanation
Correct answer: D
Explanation
the correct answer is option 4 i.e ₹8,000
In both cases, the principal amount and interest rate are the same, assumed as 'P' and 'R' respectively.
⇒ 14400 = P(1 + R/100)2 .............(i)
⇒ 25920 = P(1 + R/100)4 .............(ii)
Eq.(i) divided by Eq.(ii).
⇒ 14400/25920 = P(1 + R/100)2/P(1 + R/100)4
⇒ 5/9 = (1 + R/100)2/(1 + R/100)4
⇒ 5/9 =1/(1 + R/100)2
⇒ (1 + R/100)2 = 9/5...................(iii)
Put Eq. (iii) in Eq.(i).
⇒ 14400 = P × 9/5
⇒ 1600 = P × 1/5
Sum invested initially = P = 8000