14.A sum of money at compound interest amounts to four times of itself in 2 years. In how
many years will it be 16 times of itself?
Answers
Answer:
the answer is 16
Step-by-step explanation:
When interest is compounded, Amount A=P(1+
100
R
)
n
Given, 2P=P(1+
100
R
)
4
=>2=(1+
100
R
)
4
--- (1)
And, 16P=P(1+
100
R
)
n
=>16=(1+
100
R
)
n
=>2
4
=(1+
100
R
)
n
From eqn 1
=>((1+
100
R
)
4
)
4
=(1+
100
R
)
n
=>(1+
100
R
)
16
=(1+
100
R
)
n
=>n=16
Answer:
Step-by-step explanation:
Let principal =Rs. X
Given: amount = 4 * principal in n= 2 years
=4X
to find: No. of years N=? when amount=16* principal
solution: Amount = p(1+ r/100)^n
4X = X(1+ r/100)^2
4 =(1+ r/100)^2
taking square roots on both sides we get,
2 = 1+ r/100
2-1 = r/100
1 = r/100
r= 100%
No. of years N , when amount is 16 times of principal i.e. Amount = 16X
Amount= P( 1 + r/100) ^N
16X= X (1 + 100/100) ^N
16= (1+1)^N
16= 2^N
2^4=2^N
powers are equal when base are equal,
N=4 years
answer: In 4 years Amount will be 16 times its principal
