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The time in which a sum of money will be double at 5% p.a C.I is
- a)Rs. 10 years
- b)12 yrs.
- c)14.2 years
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The time in which a sum of money will be double at 5% p.a C.I isa)Rs. ...
2=(1+0.05)^n
ln(2)=n*ln(1.05)
n=ln(2)/ln(1.05)=14.2
Most Upvoted Answer
The time in which a sum of money will be double at 5% p.a C.I isa)Rs. ...
Solution:
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)
Where,
A = final amount
P = principal amount
r = annual interest rate
n = number of times the interest is compounded per year
t = number of years
Given, we need to find the time in which a sum of money will be double at 5% p.a C.I
Let the principal amount be P
Then, the final amount after time t will be 2P (as we need to double the amount)
So, using the formula of C.I, we get:
2P = P(1 + 5/100)^t
Simplifying this equation, we get:
2 = (1.05)^t
Taking log on both sides, we get:
log2 = t log(1.05)
t = log2 / log(1.05)
t = 14.2 years (approx)
Therefore, the correct option is (c) 14.2 years.
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)
Where,
A = final amount
P = principal amount
r = annual interest rate
n = number of times the interest is compounded per year
t = number of years
Given, we need to find the time in which a sum of money will be double at 5% p.a C.I
Let the principal amount be P
Then, the final amount after time t will be 2P (as we need to double the amount)
So, using the formula of C.I, we get:
2P = P(1 + 5/100)^t
Simplifying this equation, we get:
2 = (1.05)^t
Taking log on both sides, we get:
log2 = t log(1.05)
t = log2 / log(1.05)
t = 14.2 years (approx)
Therefore, the correct option is (c) 14.2 years.
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