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N how many years a sum of money treble at 5% p.a. compound interest payable on half-yearly rests ? (a) 18 years 7 months (b) 18 years 6 months (c) 18 years 8 months (d) None of these?
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N how many years a sum of money treble at 5% p.a. compound interest pa...
Solution:
Given, rate of interest (r) = 5% p.a.
Time period (t) to treble the amount = ?
Let the sum of money be P.
We know that,
Amount after n years, A = P(1 + r/n)^(nt)
Let the amount after t years be 3P. Then,
3P = P(1 + 5/2*100)^(2t)
3 = (1 + 5/200)^(2t)
Taking log on both sides,
log 3 = 2t log(1 + 5/200)
t = log 3/(2 log(1 + 5/200))
t = 18 years 8 months (approx)
Therefore, the correct answer is option (c) 18 years 8 months.
Explanation:
To solve this problem, we use the formula for compound interest and solve for the time period required to treble the amount. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time period.
Here, we are given that the rate of interest is 5% p.a. and we need to find the time period required to treble the amount. We can assume the principal to be P and the amount after t years to be 3P. Substituting these values in the formula, we get:
3P = P(1 + 5/2*100)^(2t)
Simplifying this equation, we get:
3 = (1 + 5/200)^(2t)
Taking log on both sides, we get:
log 3 = 2t log(1 + 5/200)
Solving for t, we get:
t = log 3/(2 log(1 + 5/200))
Substituting the values, we get:
t = 18 years 8 months (approx)
Therefore, the correct answer is option (c) 18 years 8 months.
Given, rate of interest (r) = 5% p.a.
Time period (t) to treble the amount = ?
Let the sum of money be P.
We know that,
Amount after n years, A = P(1 + r/n)^(nt)
Let the amount after t years be 3P. Then,
3P = P(1 + 5/2*100)^(2t)
3 = (1 + 5/200)^(2t)
Taking log on both sides,
log 3 = 2t log(1 + 5/200)
t = log 3/(2 log(1 + 5/200))
t = 18 years 8 months (approx)
Therefore, the correct answer is option (c) 18 years 8 months.
Explanation:
To solve this problem, we use the formula for compound interest and solve for the time period required to treble the amount. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time period.
Here, we are given that the rate of interest is 5% p.a. and we need to find the time period required to treble the amount. We can assume the principal to be P and the amount after t years to be 3P. Substituting these values in the formula, we get:
3P = P(1 + 5/2*100)^(2t)
Simplifying this equation, we get:
3 = (1 + 5/200)^(2t)
Taking log on both sides, we get:
log 3 = 2t log(1 + 5/200)
Solving for t, we get:
t = log 3/(2 log(1 + 5/200))
Substituting the values, we get:
t = 18 years 8 months (approx)
Therefore, the correct answer is option (c) 18 years 8 months.
Community Answer
N how many years a sum of money treble at 5% p.a. compound interest pa...
D none of these
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