At what rate of compound interest per annum will a sum of Rs 1348.32 in 2 years?

Discussion :: Compound Interest - General Questions (Q.No.7)

At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?

[A].	6%
[B].	6.5%
[C].	7%
[D].	7.5%

Answer: Option A

Explanation:

Let the rate be R% p.a.

Then, 1200 x		1 +	R		2	= 1348.32
100

		1 +	R		2	=	134832	=	11236
100	120000	10000

		1 +	R		2	=		106		2
100	100

1 +	R	=	106
100	100

R = 6%

Harika said: (Mar 5, 2011)
To find cp=p(1+R/100)^n-p but only amount is taken

Jasika said: (May 9, 2011)
1348.32 is CI, but here they have taken. Directly at the place of amount. ?

Vinoth said: (Aug 4, 2011)
Divide numerator and denominater by 100 to take out point. Tahts why 1200 as 120000.

Pawan said: (Oct 11, 2011)
Shakti borrows an amount of Rs 28000 for 2 years from a bank at a subsidised rate. At the end of 2 years he pays a sum of Rs 30870. How much was the rate of interest? What is the amount that should be paid if Shakti pays it after 3 years? Solve it please?

G NARESH said: (Apr 10, 2012)
How you got 11236/10000?

Pinky said: (Aug 5, 2013)
By dividing numerator and denominator by 12 we got 11236/10000.

Praveen said: (Aug 29, 2013)
Let subtract sum from total amount 1348.32 - 1200 is 148.32. 148.32 is two years interest amt (profit) we get. Ten one year interest amount is 148.30/2 = 74 per annum. Lets find the 74 amount interest rate of 1200 >>> 10% is 120 and then 6% is 74 Rs that all. 6% is right answer. Hope you understand this.

Rosy said: (Oct 16, 2013)
1348.32 = 1200(1+R/100)^2. 1.1236 = (1+R/100)^2. (1.1236)^(1/2) = (1+R/100). Since, divided half both sides, 1.06 = (1+R/100). r = 6%.

Mounica said: (Dec 11, 2013)
Can any one explain this? 1348.32 is CI, but here they have taken directly at the place of amount?

Vaibhav Patil Jadhv said: (Mar 14, 2014)

@Mounika. They didn't said 1348.32 is the compound interest they asked at what rate of the compound interest per annum the sum becomes 1348.32 from 1200 i.e 1348.32 can be equated to amount. C.I = amount-sum. Amount=sum(1+r/100)^t as the interest is compounded yearly.

Good luck.

Shikhar Shukla said: (Jul 6, 2014)
After the last step how 6% comes please explain?

Narayana Rao Gartam said: (Aug 22, 2014)
Hai Shikhar, 1+R/100= 106/100. 100+R/100 = 106/100. 100+R= 106 ( 100 AND 100 CANCELLED EACH OTHER). S0, R= 106-100. i.e: 6. I'm sure this would help you.

Madhu said: (Aug 8, 2015)
How to find the root of 11236?

Zahir said: (Nov 5, 2015)
1348.32-1200 = 148.32. Now, 148.32/1200*100 = 148.32/12 which is greater than 12% but less than 13%. So for 2 years of effective compound interests, annual interest must be greater than 6% but less than 6.5% (as 6.5% would lead effective interest to somewhere greater than 13%). So, given options answer must be 6%. Answer: 6%.

TKB said: (Feb 13, 2016)
Can't we just apply the formula P = R/T using 1200 as the principal amount?

Mounika said: (Apr 24, 2016)
Please share short cut method for this type of problems.

Naresh said: (May 12, 2016)
@Pinky. You said that divide numerator and denominator by 12 we got 11236/10000. My doubt is why we have to divide it by 12, please tell me the reason.

Anilkumar said: (May 12, 2016)
@Naresh it is divided by 12 since it is easy that way, also, it gives a perfect square of 106 & 100. One more important point you can divide both the numbers with any number, but we use specific numbers since they give a perfect square or else you can use any number to solve that problem.

Rakesh Sharma said: (Jul 15, 2016)

(100 + R) x 1200/100 = 1348.32, 100 + R = 1348.32 x 100/1200, 100 + R = 112.36,

R =12.36 * 6 + 6 + (6x6/100) = 12.36 so ans is 6.

Vijay said: (Sep 28, 2016)
1348.32 is not the C.I. It is the amount so obviously 1348.32 =1200(1 + r/100)^2,the formula for the amount,I got confused at this. Please help me.

Charu said: (Oct 6, 2016)
This method will take time because we need to think the square root that number. There is one formula for rate and i.e. 2 * ci - si * 100/si. But in this question how we'll able to find si?

Arulmozhi Nathan said: (Oct 14, 2016)
I can't understand this problem could please anyone explain for me?

Raj said: (Oct 15, 2016)
@Praveen you are right.

Hrushi said: (May 27, 2017)
I am not getting this, please can anyone explain it for me?

Prerna said: (Jun 19, 2017)
How we got 106/100?

Sravan said: (Jul 3, 2017)
The solution is 7, let me tell how check it out, This is my own formulae. A+B+AB/100 believe me it works, take 7+7+77/100=14.49, Total amount in % 14.49= 1214.49 =173.88 he asket for 2 years so 173.882 = 347.76 so got it so 7% is correct answer.

Linka said: (Jul 11, 2017)
How to find the root of 11236 in an easyway? Anyone help me out.

Krishna said: (Sep 10, 2017)
Can you please explain the step how are is 6%?

Saumitr K said: (Sep 27, 2017)
Can any one explain me how to solve it by percentage change? I am getting 6.3.

Divya said: (Dec 17, 2017)
6% how? Please explain me.

Praveena said: (Aug 4, 2018)
1+R/100=106/100. R/100=106/100-1, R/100=106-100/100, R/100=6/100, 100R=600, R=6.

Aarav said: (Aug 31, 2018)
Give shortcut to get the answer clearly.

Suraj said: (Oct 14, 2018)
What is the answer, if 9 months is given here instead of 2 years?

Saikat Ghosh said: (Oct 15, 2018)

@Linka. The shortcut method to find the Square root of 11236 is: 1*1=1, 2*2=4, 3*3=9, 4*4=16, 5*5=25, 6*6=36, 7*7=49, 8*8=64, 9*9=64, 10*10=100, 11*11=121, 12*12=144.. At first, see the last no i.e 6. So 6 can be found either in 4 square or in 6 square. Now, look at the first three numbers i.e. 112 which is near to square 10 as the square root of 11 will be more. So 10*(10+1)=110. Now see that 112<110.

So 6 square will be taken. Therefore square root of 11236 is 106.