A certain amount of money becomes thrice in 5 years at compound interest. How many years it will take to become 9 times?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 10 years
Let Principal be P.
Rate of interest = r%
Number of years (t) = 5
Amount (A) = 3P
Amount = P(1 + r/100)t
Now,
⇒ 3P = P × (1 + r/100)5
⇒ (1 + r/100)5 = 3 ...(1
Now,
Principal = P
Rate of interest = r%
Number of years = x
Amount = 9P
According to the question -
⇒ 9P = P(1 + r/100)x
⇒ (1 + r/100)x = 9
⇒ (1 + r/100)x = 32
⇒ (1 + r/100)x = {(1 + r/100)5)2
⇒ (1 + r/100)x = (1 + r/100)10
⇒ x = 10 years