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In how many years a sum of money trebles at 5% p.a. compound interest payable on half yearly basis?
- a)18 years 7 months
- b)18 years 6 months
- c)18 years 8 months
- d)22 years 3 months
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In how many years a sum of money trebles at 5% p.a. compound interest ...
Given data:
Rate of interest= 5% p.a.
Interest is compounded half yearly.
To find: Time taken for a sum of money to treble.
Formula used:
Amount= P(1+R/2/100)^(2n)
Where,
P= Principal amount
R= Rate of interest
n= Time in years
Calculation:
Let the principal amount be P.
After 1st half year, the amount becomes P(1+5/2/100)=P(21/20)
After 2nd half year, the amount becomes P(21/20)(21/20)=P(441/400)
After 3rd half year, the amount becomes P(441/400)(21/20)=P(9261/8000)
Similarly, the amount after n half years will be P(1+5/2/100)^(2n).
As we know the amount should be triple, we can write the equation as:
P(1+5/2/100)^(2n)=3P
(1+5/2/100)^(2n)=3
(1+0.025)^2n=3
(1.025)^2n=3
Take log on both sides:
2n log(1.025)=log3
n=(log3)/(2log1.025)
n=22.25 years
Hence, the time taken for the sum to treble at 5% p.a. compound interest payable half yearly is 22 years 3 months.
Therefore, option (D) is the correct answer.
Rate of interest= 5% p.a.
Interest is compounded half yearly.
To find: Time taken for a sum of money to treble.
Formula used:
Amount= P(1+R/2/100)^(2n)
Where,
P= Principal amount
R= Rate of interest
n= Time in years
Calculation:
Let the principal amount be P.
After 1st half year, the amount becomes P(1+5/2/100)=P(21/20)
After 2nd half year, the amount becomes P(21/20)(21/20)=P(441/400)
After 3rd half year, the amount becomes P(441/400)(21/20)=P(9261/8000)
Similarly, the amount after n half years will be P(1+5/2/100)^(2n).
As we know the amount should be triple, we can write the equation as:
P(1+5/2/100)^(2n)=3P
(1+5/2/100)^(2n)=3
(1+0.025)^2n=3
(1.025)^2n=3
Take log on both sides:
2n log(1.025)=log3
n=(log3)/(2log1.025)
n=22.25 years
Hence, the time taken for the sum to treble at 5% p.a. compound interest payable half yearly is 22 years 3 months.
Therefore, option (D) is the correct answer.
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Community Answer
In how many years a sum of money trebles at 5% p.a. compound interest ...
Let, Principal= 100 and Amt.=300
r= 0.05/2= 0.025
t=n×2 .•. t = n/2
now, using the formula A=P (1+i)^n
we get,
300=100 (1+ 0.025)^n
3= 1.025^n
n=44.5 (approx.)
t=n/2
= 44.5/2
= 22.25 (approx.) hence 22yrs 3 months
r= 0.05/2= 0.025
t=n×2 .•. t = n/2
now, using the formula A=P (1+i)^n
we get,
300=100 (1+ 0.025)^n
3= 1.025^n
n=44.5 (approx.)
t=n/2
= 44.5/2
= 22.25 (approx.) hence 22yrs 3 months
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In how many years a sum of money trebles at 5% p.a. compound interest payable on half yearly basis?a)18 years 7 monthsb)18 years 6 monthsc)18 years 8 monthsd)22 years 3 monthsCorrect answer is option 'D'. Can you explain this answer?
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