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In how many years a sum of money trebles at 5% p.a. compound interest payable on half-
yearly basis?
yearly basis?
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In how many years a sum of money trebles at 5% p.a. compound interest ...
Calculation of time taken to triple the amount with compound interest
Compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount
r = Rate of interest
n = Number of times interest is compounded per year
t = Time in years
Given data:
Rate of interest (r) = 5% = 0.05
Number of times interest is compounded per year (n) = 2 (half-yearly)
Amount is to be tripled, so A = 3P
Substitute the values in the compound interest formula:
3P = P(1 + 0.05/2)^(2t)
3 = (1 + 0.025)^(2t)
3 = (1.025)^(2t)
Take log on both sides:
log 3 = log (1.025)^(2t)
log 3 = 2t * log (1.025)
t = log 3 / (2 * log 1.025)
Calculating the time:
t = log 3 / (2 * log 1.025)
t = 21.96 years
Therefore, it will take approximately 21.96 years for the sum of money to triple at a 5% p.a. compound interest rate payable on a half-yearly basis.
Compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount
r = Rate of interest
n = Number of times interest is compounded per year
t = Time in years
Given data:
Rate of interest (r) = 5% = 0.05
Number of times interest is compounded per year (n) = 2 (half-yearly)
Amount is to be tripled, so A = 3P
Substitute the values in the compound interest formula:
3P = P(1 + 0.05/2)^(2t)
3 = (1 + 0.025)^(2t)
3 = (1.025)^(2t)
Take log on both sides:
log 3 = log (1.025)^(2t)
log 3 = 2t * log (1.025)
t = log 3 / (2 * log 1.025)
Calculating the time:
t = log 3 / (2 * log 1.025)
t = 21.96 years
Therefore, it will take approximately 21.96 years for the sum of money to triple at a 5% p.a. compound interest rate payable on a half-yearly basis.
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In how many years a sum of money trebles at 5% p.a. compound interest payable on half- yearly basis?
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In how many years a sum of money trebles at 5% p.a. compound interest payable on half- yearly basis? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In how many years a sum of money trebles at 5% p.a. compound interest payable on half- yearly basis? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many years a sum of money trebles at 5% p.a. compound interest payable on half- yearly basis?.
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