Related The time required for a sum of money to amount to five times itself at 16% simple interest p.a. will bea)25 yearsb)20 yearsc)15 yearsd)18 yearsCorrect answer is option 'A'. Can you explain this answer?
GIVEN:
Rate of Interest = 16%
FORMULA USED:
Simple Interest = (P × R × T)/100
CALCULATION:
Let Principal = x
Amount = 5x
Simple Interest = 5x - x=4x
Simple Interest = (P × R × T)/100
4x = (x × 16 × T)/100
T = 25 years.
Alternate method:
Principal (100) → amount (500)
So, interest = 500 - 100 = 400 @ 16%
Therefore, required time = 400/16 = 25 years
Solution
Let, Principal amount be P.
Rate of interest be R per annum.
Time of investment is (T)=12 years.
Sum of the money becomes three times in 12 years.
⇒A=3P.
⇒A=P+(P×T×R100)
⇒3P=P(1+T×R100)
⇒3=1+12×R100
⇒3−1=12R100
⇒2=3R25
⇒50=3R
⇒503=R
Now, we need to find the number of years T such that, Sum of the money becomes five times.
⇒5P=P(1+T×R100)
⇒5=1+T×503×100
⇒5−1=T×13×2
⇒4=T6
⇒24=T
will it become 5
times at the same rate of simple interest 24 years.