GIVEN: A sum of Rs. P becomes Rs. 3P in 5 years when invested at compound interest.
CONCEPT: Compound interest concept.
FORMULA USED: Amount
=P×(1+)T Where,
P = Principal, R = Rate, T = Time
CALCULATION: Principal = Rs. P,
⇒ Amount after 5 years = 3P
According to the question,
3P=P×(1+)5 ⇒
(1+)5=3−−−−(i) Now,
Time = 15
⇒
A=P×(1+)15 ⇒
A=P×[(1+)5]3 From equation (i):
A =
P×33 ⇒ A = 27P
∴ The sum will be 27P times after 15 years.
Short Trick In case of Compound interest:
If a sum becomes ‘x’ times in ‘t’ years:
It will be
‘x2’ times in ‘2t’ years.
It will be ‘
x3 ’ times in ‘3t’ years and so on.
Hence,
A sum becomes 3 times in 5 years when invested at compound interest, it will be
27(=33) times in
15(=3×5) years