A certain amount, when put at a compound rate of interest, becomes double in 5 years. In how many years will the amount become eight times?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 15 years
Under compound interest the amount is multiplied by the same factor in every equal period, because each year’s interest is earned on the amount already grown. If the amount doubles in 5 years, it doubles again in every further 5 years.
Eight times is \(2\times2\times2=2^3\), so the sum must double three times
After 5 years the amount is 2 times the sum, after 10 years \(2\times2=4\) times, after 15 years \(4\times2=8\) times
Three doubling periods of 5 years each take \(3\times5=15\) years