Aptitude - Compound Interest - Discussion

5. 

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:

[A]. 2
[B].
2 1
2
[C]. 3
[D]. 4

Answer: Option A

Explanation:

Amount = Rs. (30000 + 4347) = Rs. 34347.

Let the time be n years.

Then, 30000 1 + 7 n = 34347
100

107 n = 34347 = 11449 = 107 2
100 30000 10000 100

n = 2 years.


Chaitu said: (Nov 23, 2010)  
30000(107/100)=32100
(32100*7)/100=147 is for 1 year
2100+2100+147=4347

2 years

Lalitha said: (Mar 25, 2011)  
Can any one please help how it has come (107/100)^2

Dittya said: (Apr 5, 2011)  
Yaa, its because (107)^2 = 11449 and (100)^2 = 10000.

Prabakaran said: (Jul 19, 2011)  
What is 107/100 ?

Anusha said: (Oct 16, 2011)  
Amount=30000+4347 = 34347
amount=p(1+R/100)^n
34347=30000(1+7/100)^n
34347=30000(107/100)^n
34347/30000=(107/100)^n
11429/10000=(107/100)^n.
hence
(107/100)^2=11429/10000.

Mercy said: (Jan 20, 2012)  
Simpler yet old-fashioned solution to me would be:

30000*7/100=2100 - year 1
30000+2100=32100*7/100=2247 - year 2
now add 2100+2247=4347 which was the compound interest earned after 2years.

Thus the ans is 2 years.

Swa1 said: (Aug 22, 2012)  
4347=30,000(1+7/100)^n why not?
and 30,000+4347=34,347 why?
plz any one explian me.

Usha said: (Sep 14, 2013)  
C.I will be the 4347.

C.I = AMOUNT-PRINCIPAL.

PRINCIPAL = 30,000.

4347 = AMOUNT-30000.

AMOUNT = 4347+30000 = 34347.

AMOUNT = P(1+R/100)^n.

34347 = 30000(1+7/100)^n.

34347/30000 = (107/100)^n.

Sumit P. said: (Oct 25, 2013)  
Sorry Guys but it should;

11449 / 10000 // 34347 / 30000 is multiplied and divide by 3.

Hence, Now 11449 and 10000 are squares of 107 and 100 resp.

Thus(107 / 100)^ 2. Thus n = 2.

Anshu said: (Dec 20, 2013)  
30000*7/100 = 2100 - year 1.

30000+2100 = 32100*7/100 = 2247 - year 2.

Now add 2100+2247 = 4347 which is 2 years.

Hafsa Ali said: (Jan 2, 2014)  
Why we add 30,000 and 4347?

Arpita Dey said: (Feb 26, 2014)  
How (107/100)^t = 34347/30000.

t=2?

I forgot the conversion.

Manasa said: (Mar 7, 2014)  
What is the shortcut method for calculating the square root of 11449?

Fizna said: (Nov 19, 2014)  
Can anyone say the exact formula for finding the period?

Hitendra said: (Dec 2, 2014)  
How to calculate (107/100)^t = 34347/30000?

Rajnish said: (Dec 11, 2014)  
Hi guys,

I think (107/100)^t is not easy to find without using calculator.

So, I want advice you play hit and trial. Take t = 1, t = 2, ..... and match your option.

Tejas said: (Dec 15, 2014)  
Why 34347/30000?

Digvijay said: (Dec 18, 2014)  
Ya! it's not easy to find out. We have to try with value of t.

Isha Sharma said: (May 9, 2015)  
Guys this is simple divide numerator and denominator by 3 you will get your answer.

Trilok said: (Sep 14, 2015)  
11449/10000 = (107/100)^n , 1.1442 = (1.07)^n.

We can write as log 1.1442 = n log 1.07, n = log 1.1442/log 1.07 = 0.058501/0.029383 = 2 (as per scientific calculator).

Bhabani said: (Oct 20, 2015)  
A sum becomes double in ten years in C.I. So in how many years the principal would be 8 times?

Leo said: (Nov 28, 2015)  
Can anyone explain me the simplification of (107/100)2?

Abhilok said: (Dec 6, 2015)  
2 times in 10 years.
2^3 = 8 times in 3*10 = 30 years.

Let power = n.
Given year = y.
n*y is the answer.

Dearlie Beloved said: (Dec 30, 2015)  
Shortcut through using ln:

t = ln (34 347/30 000)/ln (1.07).
t = 2 years.

Anurag Nath said: (May 12, 2016)  
@Hitendra.

(107/100)n = 11449/10000.
=> 107 * 107/100 * 100 = 11449/10000.
=> (107/100)2 = 11449/10000 [Here n = 2].

Therefore n=2.

France said: (Jun 28, 2016)  
107 * 107 is 11449 and 100 * 100 = 10000 but how is it equal to 34347/30000 ?

Rkh said: (Nov 14, 2016)  
What if the power is( 107/100)^4?.

How can we find quad root of a number?

Chloe said: (Mar 27, 2017)  
Use the formula

n = [ log(fv/p) ] / [ log (1+i)].

Where
FV = future value.
P = present value.
i = interest ( in dec. place).

n = [ log ( 34,347/30,000) ] / [ log (1+0.07)].
= 2.

B. Tatung said: (May 9, 2017)  
How come 3 divided by both numerator and denominator?

Please, someone, explain me.

Akash Kumar Sinha said: (Jul 14, 2017)  
1st year CI= 7% OF 30000 ie 2100.
2nd year CI=2100+ 7% of 2100 ie 147.
2100+2100+147=4347.
Hence, 2 years.

Priya said: (Jul 29, 2017)  
What is 107/100? I can't understand, please explain.

Shipra said: (Aug 2, 2017)  
Thanks people. It helped a lot!

Subramanyam said: (Aug 23, 2017)  
Thanks, friends. It helped a lot!

Narsim Bari said: (Feb 27, 2018)  
30000*7/100 = 2100 for 1rst year.
For 2nd year : 30000+2100*7/100 = 2247.

Now, cross-check the given calculated amount given in the question itself i.e 4347 rupees by adding 2 years amount (2100+2247)=4347.

Believe this is the fastest and tricky method of our natural mind.

Prasad said: (Jun 15, 2018)  
Why we square that 107/100 n=2? why? please.

Sangavi said: (Dec 9, 2018)  
Why we add 30000 and 4347, can anyone please explain it?

Bimla Jarmwal said: (Jan 4, 2019)  
Please, anyone, explain the answer in detail to me.

Anomie said: (Jan 29, 2019)  
How did come 11449?

Lokesh said: (Mar 21, 2019)  
Verify with given option.
CI =7 %
1ST YEAR 7%.

For 2nd year, it becomes 7.49
Total 14.49
If 100% = 30K.
Then 114.49 = ?
(114.49 * 30K)รท100.

And you will get 4347.

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