If the simple interest earned on a certain sum for the 1 year is Rs 2,000 and compound interest earned in 2 years is Rs 4,160 then, what will be the rate of interest?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 8.
Simple interest:
S.I. = (P × R × T)/100
⇒ (P × R × T)/100 = 2000
⇒ P × R = 200000...........(1)
Compound interest:
C.I. = P(1 + (R/100)2) - P
⇒ P(1 + (R/100)² - 1) = 4160
⇒ P(1 + (R/100)²) = 4160
⇒ P[(200 + R)(R)]/1002 = 4160
⇒ P[(200 + R)(R)] = 41600000...........(2)
Dividing both equations, we have
⇒ 1/(R + 200) = 20/4160
⇒ R + 200 = 208
⇒ R = 8%