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Simple and Compound Interest
by Total Gadha - Sunday, 15 April 2007, 01:00 PM
 

CAT 2010 MBA Simple Interest (SI) Compound Interest (CI)Every MBA aspirant who understands percentages and the principles of arithmetic and geometric progressions will be able to handle problems of simple interest (SI) and compound interest (CI) easily. In CAT, XAT or other MBA exams, the problems on simple and compound interest are asked as a part of percentages only. Let me start this lesson with a simple problem:   

                                                    CAT MBA Simple Interest (SI) Compound Interest (CI)

Tommy and his dad planted two plants on the same day. The first plant is 10 ft high and grows by 10 ft every day. The second plant is 1 ft high and doubles its height everyday. On which day will the 1 ft high plant overtake the 10 ft high plant?

Answer: Let's make a simple table to answer this question. We note down the heights of the plants on each day, as shown below:
CAT MBA Simple Interest (SI) Compound Interest (CI)
We can see from the table that the 2nd plant outgrows the 1st plant on the 8th day (colored orange in the table). Now, answer the following questions:

1.       Which plant has a fixed increase in height everyday? How much is this increase?
2.      
Which plant is growing at a faster rate?
3.      
What is the percentage increase in the height of 2nd plant everyday?
4.      
What will be the difference in heights of the plants on the 10th day?

You can see that the 1st plant has a fixed increase of 10 ft in its height everyday. If you observe harder, this increase of 10 ft is nothing but 100 % of its original height. Therefore, the 1st plant is increasing with a fixed percentage of its original value. In other words, the first plant is growing with a simple interest (SI) rate.

CAT MBA Simple Interest (SI) Compound Interest (CI)

You can also see that the 2nd plant is increasing at a faster rate and increases by 100% on its present value everyday. In other words, the second plant is increasing at a compound interest (CI) rate.

CAT MBA Simple Interest (SI) Compound Interest (CI)

Therefore, both the plants are increasing by the same percentage, first on the initial value and the second on the current value. Hence, the first is in simple interest and the second is in the compound interest.

Note that the heights of the 1st plant form an arithmetic progression with a common difference of 10 ft and the heights of the second plant form a geometric progression with a common ratio of 2.

Therefore, to calculate the heights on the 10th day we use the formula for the Nth terms of the arithmetic and geometric progressions.

For the 1st plant

Tn = a + (n - 1)d --> T10 = 10 + 9 x 10 = 100

For the 2nd plant

Tn = arn - 1 --> T10 = 1 x 29 = 512.

Therefore difference in heights = 512 - 100 = 412 ft

CAT MBA Simple Interest (SI) Compound Interest (CI)

This time, we invest the two amounts of Rs100 each, both at the annual rate of 10%, one at simple interest and the other at compound interest. Let's see their growth:

CAT MBA Simple Interest (SI) Compound Interest (CI)

Notice a few things:

CAT MBA Simple Interest (SI) Compount Interest (CI) 

SOME SOLVED EXAMPLES:

1.       In how many years will an amount invested in simple interest at the rate of 5% get doubled?

Answer: we know that yearly amounts in a simple interest scheme are in arithmetic progression with common difference of Pr/100. In this case, the amounts will be in arithmetic progression with a common difference of 0.05P.

The series is P, 1.05P, 1.1P, 1.15P, … (P + n x 0.05P), ...and so on. Let the amount be double of the original amount after n years.
Therefore, P + n
x 0.05P = 2P --> n = 20 years.

Alternative Answer: The amount is growing by 5% every year or 1/20th every year. Since 1/20th of the sum is added every year, the whole sum will be added in 20 years.

CAT MBA Simple Interest (SI) Compound Interest (CI) 


I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some problems based on this in the CBT Club this week.

 

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Re: Simple and Compound Interest
by Puneet Kabra - Thursday, 10 May 2007, 11:44 PM
 

Hi TG smile

I think the answer for Question 5 is incorrect. My Calculations are as follows:

Rajan borrowed Rs.7000/- from the bank at 5% SI.

Now, the SI per year for Rs.7000/- will be Rs.350/-

This has to be paid by Rajan.

After 2 yrs, he pays Rs.4000/- which comprises of Interest of Rs.700/- and Principal of Rs.3300/-

Now, the Principal for remaining 3 yrs becomes Rs.3700/-

For this principal, he'll have to pay an Interest of Rs.185/- per yr for 3 yrs.

So the remaining amount he will have to pay the bank at the end of 5 yrs will be [Rs.3700(Principal) + Rs.555(Interest for 3 yrs)] = Rs.4255/-

 

 

Re: Simple and Compound Interest
by Total Gadha - Sunday, 13 May 2007, 10:06 AM
  Hi Puneet,

This is the reason I explained the problem. Most people use this method of finding out amount to be paid till that time, subtract the amount paid, and then create a new principal for the remaining period of time. And that is NOT correct. Think about it this way- If you borrowed this money from your friend he would expect to recieve Rs8750 at the end, but you are paying him only Rs8255. Is it fair?

Total Gadha

Re: Simple and Compound Interest
by shiwa k - Thursday, 24 May 2007, 05:15 PM
 

hi tg,

which method is right..

y should we not create another principal for the remaining period.?

im confused... clear my doubt. plz

 

thanks

Re: Simple and Compound Interest
by amir khan - Friday, 20 July 2007, 10:13 PM
 

question3

solution: using trick given in career launcher guide,we know that

for same rate and principal invested,

SI for 2 years/CI for 2 years=(2/(2+r%))

now r% given=10

therefore ratio will be 2/12=1/6

or 6*SI=CI

also, CI-SI=200(given)

OR, 6SI-SI=200

OR, SI=40

NOW using SI formula we can get principal equals to 200

but answr is 20000

why i am getting wrong answer?????

Re: Simple and Compound Interest
by Total Gadha - Saturday, 21 July 2007, 02:16 AM
  SI/CI = 200/(200 + r)
Re: Simple and Compound Interest
by DEEPAK KANSAL - Monday, 30 July 2007, 05:10 PM
 

hi TG

the freind has given 4000 at end of  2 years and he will earn a interest of Rs 600 for the remaining 3 years (as calulated by u in Q.5 for the bank)

thus total amount piad = 4225+ 4000+ 600 =8825 which is more than 8750...

pl explain TG which is correct.....

Re: Simple and Compound Interest
by The Phoenix - Wednesday, 8 August 2007, 07:46 PM
 

Hi Deepak,

I will trya explain the situation. Hope this will clear ur doubt.

The initial money you took is 7000 bucks. Out of which you have returned 4000 bucks at the end of 2 years. So, effectively, you have to pay him the interest of that 4000 for 2 years which is 4000*5*2/100, which is 400.

Now for the remaining 3000, you have to pay the interest of the whole 5 years. So, that would sum up to 3000*5*5/100,which is 750.

So, the total interest u gotta pay is 750+400 = 1150. Apart from this, u have to pay the principal amount which is 7000. So, on the whole, you have to pay him 7000+1140 = 8140. Out of which,you have paid 4000. So, the remaining amount u have to pay is 8140 - 4000 = 4150.

Am I right TG sir?

 

Installments
by Mou Sukoshi - Saturday, 3 November 2007, 01:17 PM
 

Hi TG,

can u plz gv the formulas for installments ..... both for simple and compund interest cases?

Re: Simple and Compound Interest
by Abhishek Kapoor - Thursday, 15 November 2007, 07:02 PM
 

hi,

I believe we shld calculate interest on 7000 for 2 yrs and subtract the amt from 4000/-. Int (rs 700)

this will fetch as a new principal - rs 3700/- (7000-3300)

on this principal we shld calculate int i.e 3700*3*5/100 and add it to 3700 to find the balance amt to be paid.

Re: Simple and Compound Interest
by Bajrang Gupta - Tuesday, 24 June 2008, 01:30 PM
 

I am pretty late in replying to the post, as it seems outdated. However, I would like to make a point for others who would be looking ahead...

@The Phoenix -> The 4000 you borrowed and returned at the end of 2 years. However, where is the interest on that 4000. You cannot say that you will return it after 5 years. I think thats the miss.

To give it a new direction, I think we should consider the SI to be a fixed kind of investment. And any form of repayment has to be treated as a new investment. It is also a practical approach followed by banks for providing loans.

 

 

 

Re: Simple and Compound Interest
by Mukund Jn - Tuesday, 22 July 2008, 04:18 PM
  plz give something about instalments, both with SI and CI. also any short cut method welcome. questions like sum borrowed and instalment amount is asked.
Re: Simple and Compound Interest
by vikas sharma - Monday, 16 February 2009, 10:40 AM
 

hi i think for first 2 years interest will be on amount Rs7000 ie 7000*2*5/100 is rs 700,after paying 4000 interest will be on rs 3000 for next three years ie3000*3*5/100 is rs450 .So total interest is 700+450=1150

Amount he has to pay=7000+1150-4000=4150

Am i wright

Re: Simple and Compound Interest
by simran pal jaggi - Wednesday, 1 July 2009, 06:50 PM
 

Hi TG....

      this is my first ever post on total gadha.... smile

     in Q5 i think the money returned after 2 yrs(Rs 4000) should not gain any interest..as it has only been returned back to the bank and not deposited so as to gain any interest.....

what do you say ??

Re: Simple and Compound Interest
by praveen rathod - Wednesday, 8 July 2009, 08:44 PM
 

smile

hi tg,

i've another method for Q.5:

for first 2yr si=700

after paying 4000 he has to 3000+interest of 3000 for 3yr +700=3000+450+700=4150
   

Re: Simple and Compound Interest
by Subramaniam Gopalkrishnan - Wednesday, 8 July 2009, 09:44 PM
  Hey TG...
Please help to solve this..
What annual payment will discharge a debt of Rs 808 due in 2 years at 2% per
annum ?

1) Rs.200
2) Rs.300
3) Rs.400
4) Rs.350
Re: Simple and Compound Interest
by nitin niraj - Friday, 4 September 2009, 01:08 PM
  we can solve this problem by using a formula i.e
100a/100t+rt(t-1)/2
where a=annual debt
r=rate
t=time
putting the value of a=808,r=2%,r=2years
100*808/100*2+2*2(2-1)/2=80800/200+2=80800/202=400
hence option 3 is correct
Re: Simple and Compound Interest
by Siddhartha Singh - Thursday, 5 November 2009, 11:16 AM
  Hi TG,

(on Q.5 explanation by TG)
The rate at which Rajan has borrowed the money from bank(i.e 5%) and the rate at which the money grows in the bank need not be the same.
So considering that Rs.4000 for the three yrs reaps an interest of 5% per yr should be wrong.
Re: Simple and Compound Interest
by Saurabh - confusion fused - Monday, 9 November 2009, 12:38 PM
  @ Puneet:

(Guys I haven't read all the replies...so if I'm repeating the logic just ignore, I'm stating the way I solved it)

You can think like this:
He returned 4 thousand after 2 years so in fact he borrowed 7 thousand only for 2 years, so the interest on it is 700. He returned 4000 so for next 3 years he borrowed only 3000. So he should pay interest only for 3000, which is 450 rs. for 3 years. So total interest he is paying = 700 + 450 = 1150 rs.

But hey hey look what is asked, the total amount he should pay back is asked, now he also has to return the principal amount which is 3000.

So total money he has to return after 5 years (apart from 4000 he already returned)
= total interest + remaining principal amount
= 1150 + 3000
= 4150

Regards,
$aurabh
Re: Simple and Compound Interest
by reema kharbanda - Wednesday, 18 November 2009, 11:00 PM
  plz help me with this ques....
a sum of moneydoubles itself in 4 yrs at a certain rate of compound intrst..what is the rate??
Re: Simple and Compound Interest
by Pallav Jain - Thursday, 19 November 2009, 02:00 AM
  hI reema
Let P be the Principal and R be the rate to be found and N be the no of years
Here N=4. Since we are given that amount becomes 2 times in 4 years, A =2P.

A = P*(1+(R/100)) N

Since A =2P
2P = P*(1+(R/100))^4

Now you can conclude that
(1+(R/100))^4 == 2

Now you can go by options like 1.2^2 = 1.44
js take 1.4^2 = 1.96 ( which is apprx. 2 ) but we can not take it as we have ignore some fractional part so 20 can not be the answer so Answer is
19 Years.....  (1.+19/100)^4 = 1.19^4

Hope its Clear
Happy Learning !!!!!
Pallav
Re: Simple and Compound Interest
by sachi bhat - Friday, 20 November 2009, 11:09 PM
  Hi TG sir,
the analogy which you have used is simply superb
Re: Simple and Compound Interest
by abhishek rai - Thursday, 13 May 2010, 01:00 PM
  A simple yet powerful read. One question TG sir, Where are the questions that are supposed to be in CBT club?
Re: Simple and Compound Interest
by Total Gadha - Thursday, 13 May 2010, 10:33 PM
  Abhishek,

Question hi question to hain CBT Club mein. Aur hain kya? Are you not attempting the quizzes there?

Total Gadha
Re: Simple and Compound Interest
by abhishek rai - Friday, 14 May 2010, 06:32 PM
  Chapterwise questions sir...but I checked the quizzes...

They are grt sir!!!
Re: Simple and Compound Interest
by bllitz blitz - Wednesday, 26 May 2010, 09:20 PM
  Hi TG,
Can you help us in understanding the concept in this question...
"What annual payment will discharge a debt of Rs 808 due in 2 years at 2% per
annum ?" Asked by subramani sometime earlier...  I could work it out using options but want to make the concept clear.
Re: Simple and Compound Interest
by amit kheterpal - Thursday, 15 July 2010, 02:44 PM
 

Nice article Sir,Please post articles related to bionomial theorem,log,ratio and proportion etc smile

Thankyou.smile

Re: Simple and Compound Interest
by deepti anand - Thursday, 15 July 2010, 05:15 PM
  hii TG...
I hv a problem...m posting it...can u help me..

a certain sum is invested at SI. if the sum becomes k times itself in 16 years and 2k times itself in 40 years. in how many years will it become 4k times itself..??
1) 96
2)88
3)80
4)64

plz help me out...
Re: Simple and Compound Interest
by Silent killer - Thursday, 15 July 2010, 07:55 PM
  hi..
The answer is 88 years..
Soln:

In SI for the sum to become k times it takes x*(k-1)------(1)

where x is time taken for the sum to double.

we know x(k-1)=16 & x(2k-1)=40

solving u get x=8 and k=3

from eqn(1) sum becomes 4k times in = 8(12-1)=88


Am i correct?
Re: Simple and Compound Interest
by Abhirup DebRay - Thursday, 15 July 2010, 10:20 PM
  m also gtng 88 yrs
Re: Simple and Compound Interest
by Silent killer - Thursday, 15 July 2010, 11:34 PM
  hey abhirup,
please give ur solution..
Re: Simple and Compound Interest
by Abhirup DebRay - Friday, 16 July 2010, 10:54 AM
  (k-1)P=P*R*16/100
(2k-1)P=P*R*40/100
dividing we get d value of k as 3
now
(4k-1)P=PRT/100
dividing wid ny 1 of d 1st two eq & substituting k as 3
we get T=88 yrs
Re: Simple and Compound Interest
by silent killer - Saturday, 17 July 2010, 12:48 AM
  that was simple and quick..
thanks abhirup...
Re: Simple and Compound Interest
by ankur gupta - Saturday, 17 July 2010, 10:43 PM
  the concept to this question highlights the same point which TG wanted to put forth with the question Q5.

Here when we make a payment after 1st year, then that amount can become principal for the 2nd year and generates interest in the second year, which contributes in paying the debt...
So the equation becomes :

P + P + (P*2*1)/100 = 808

Solving this : P = 400.

Same in Q5, the bank requires fixed amount at the end of 5 years. Hence the 4000 returned will become principal for the remaining period and will get interest in paying back the bank.. 
Re: Simple and Compound Interest
by deepti anand - Monday, 26 July 2010, 08:23 PM
  hii all..
thanx a lot 4 the sol...
Re: Simple and Compound Interest
by jay gajjar - Friday, 24 September 2010, 02:40 PM
  show that a sum of money will increase more than 100 times in 100 years @ 5% compound interest?
Re: Simple and Compound Interest
by ajit dsouza - Sunday, 17 October 2010, 10:06 AM
  i dont agree with ur 4150 result ..... the thing is bank will not charge money for the amount he has taken . if i am wrong  kindly clear my doubt....
Re: Simple and Compound Interest Q5
by Deepak Gupta - Tuesday, 5 July 2011, 10:54 AM
  let's take Q otherway that is : Rajan deposited the sum of Rs 7000 in bank with 5% SI for period of 5 yrs.
When he withdrew Rs 4000 after 2 yrs -- Q can be reframed as Rs 7000 deposited for 1st two yrs and Rs 3000 for next 3 yrs. After 5 yrs he will get his left out pricipal of Rs 3000 + 2 yrs SI on Rs 7000 i.e. Rs 700 + 3 yrs SI on Rs 3000 i.e. Rs 450. i.e. 3000 + 700 + 450 = Rs 4150.
Note - main troubling part to understand is Rs 700 - As it's SI therefore no interest on it and it will be paid only at the end of tenure i.e. 5 yrs.
Re: Simple and Compound Interest
by satyam mishra - Wednesday, 31 August 2011, 01:19 PM
  @PRAVEEN nice, a much simpler method. thanks
Re: Simple and Compound Interest
by Mohit Sharma - Wednesday, 2 May 2012, 02:06 PM
  Hi Kamal Sir,
 Can you please explain the following ques.:
1) Some amount was lent on 6% per annum simple interest. After one year, Rs.6800 is repaid and the rest of the amount is repaid at 5% per annum. If the second year's interest is 11/20 of the first year's interest, find what amount of money was lent out.
a) 17000
b) 16800
c) 16500
d) 17500
e) None of these

2) An amount of Rs. 12820 due 3 years hence, is fully repaid in three annual installments staring 1 year. The first installment is 1/2 the second installment and the second installment is 2/3 of the third installment. If the rate of interest is 10% per annum, find the first installment.
a) 2400
b) 1800
c) 2000
d) 2500

Please explain the ans also Sir.
Re: Simple and Compound Interest
by TG Team - Wednesday, 2 May 2012, 03:41 PM
 

Hi Mohit smile

1. If x is the total amount to be paid, then

0.05(1.06x - 6800)/0.06x = 11/20

=> 100(1.06x - 6800) = 66x

=> 40x = 680000 and x = 17000. 

2. Let the installments be a, 2a, 3a, then

a(1.1²) + 2a(1.1) + 3a = 12820 (assuming interest rate is compounded annually)
a = 12820/6.41 = 2000

Kamal Lohia

Re: Simple and Compound Interest
by Mohit Sharma - Wednesday, 2 May 2012, 06:05 PM
  Thank u sir,

I really get confused with that equal payment questions. Can you throw some light on it sir.

Re: Simple and Compound Interest
by Gagan Chhabra - Wednesday, 2 May 2012, 10:04 PM
  hey guys ...
initially we hav 7000 bucks n it remains for 2yrs..so interst comes out to be 700 bucks..now 4ooo bucks he already paid.on  remaining 3000 bucks interest of 5% will be applied for 3 yrs n dat comes out to be 450
total interest = 700+450
                    = 1150
3000 still to be paid by rajan..so total amount will be 1150+3000=4150
Re: Simple and Compound Interest
by Prerna Golani - Friday, 11 May 2012, 02:10 PM
  I am unable understand why have you used 0.05(1.06x - 6800)/0.06x = 11/20,what is 1.06 x here if x is the total amount x-6800 should be used in equation
Re: Simple and Compound Interest
by Mohit Sharma - Friday, 11 May 2012, 02:16 PM
  Hi Prerna,
Here x is the total amount and 1.06x is the total amount( including interest for 1 year at 6% per annum). In next year he paid 6800/-. So remaining amount would be (1.06x-6800).

I hope you get it.
Re: Simple and Compound Interest
by amit jain - Thursday, 14 June 2012, 12:42 AM
  hi kamal,
if we compare your soln of the 1st question to the question 5 earlier solved by TG ,it seems to give two contradictory methods.
U seem to subtract 6800 from amount while TG did by subtracting from principal.
Please give ur soln of the TG question--
rajan borrowed 7000 from a bank at 5% SI.the amount is to be paid after 5 years.rajan pays 4000 after 2 years.how much should he pay after 5 years to discharge the debt completely.

Thanks,
Amit
Re: Simple and Compound Interest
by Mohit Sharma - Thursday, 14 June 2012, 01:10 AM
  Hi amit,
For your question,
rajan borrowed 7000, then interest for 2 years will be,
7000*2*5/100=700
total=7700/-
he paid 4000/- after 2 years then,remaining amount=7700-4000=3700/-
on this amt calculate interest as 3700*3*5/100=555/-
Amount he need to pay after three years= 4255/-
I hope my ans is correct.

Thanks and Regards,
Re: Simple and Compound Interest
by amit jain - Thursday, 14 June 2012, 01:05 PM
  Hi Mohit,
even my approach is same as yours,but if u look at example-5 solved by TG in theory section ,u wil see that he has solved this question differently and his answer is 4150.

Thanks
Re: Simple and Compound Interest
by TG Team - Thursday, 14 June 2012, 01:59 PM
 

Hi Amit and Mohit smile

Try to understand the question properly. It says that "the amount is to be paid after 5 years"

That means he needs to pay the interest for all the five years on the amount borrowed at the end of 5-year period. Or in other words, his due towards bank five years from now is = (7000 × 5 × 5)/100 = 8750. So, suppose if he pays some interim amount in between then that'll will not be deducted from total payable after 5 years, rather its worth after total period (calculated according to given rate of interest) will be deducted from total payable at the end of 5 years to determine the balance to-be-paid.

Now try to see the question and solution in this light. Hope it should be clear. smile

Kamal Lohia  

Re: Simple and Compound Interest
by Mohit Sharma - Thursday, 14 June 2012, 07:13 PM
  Thanks Kamal sir. Got the point now. smile
Re: Simple and Compound Interest
by amit jain - Friday, 15 June 2012, 08:29 PM
  thx a lot kamal...... big grin
Re: Simple and Compound Interest
by Sahil Jagdev - Monday, 18 June 2012, 11:41 PM
  Just calculate the S.I. on 808 for 2 yrs at 2% per annum. The S.I. Comes to be Rs.32.32.
So total amount comes to be Rs. 808+32.32= 840.32.
Now it is supposed to be disbursed into two equal amounts:

840.32/2 = 420.16 Hence the Answer.
Re: Simple and Compound Interest
by S K - Wednesday, 20 June 2012, 03:27 AM
  What about this solution for Question -5 :

He borrowed 7000 for 2years therefore interest for two years
 (7000 × 2 × 5)/100 = 700

Amount Paid after 2 years is 4000.

Hence   New Principal= Original Principal-Amount Paid =
7000-4000=3000.

Now calculating Interest on this new PRINCIPAL for remaining three years
(3000 × 3 × 5)/100 = 450

Therefor TOTAL amount that needs to be paid=

700(Interest on Old Principal for two years) +450(Interest on New Principal for remaining three years)+3000(New Principal)=4150.


Re: Simple and Compound Interest
by Aditya Pandey - Wednesday, 22 May 2013, 05:45 PM
  7000= 4000/(1+2*5/100) + P/(1+5*5/100)
Is this approach of equating present values incorrect?
Present Value P = X/(1+n*R/100)
Please explain?
Re: Simple and Compound Interest
by axhish ranj - Tuesday, 13 August 2013, 08:30 PM
  yes man you are correct this is how it should be calculated and ans should be 4235
Re: Simple and Compound Interest
by pallavi juturu - Saturday, 24 August 2013, 05:29 PM
  can you explain the concept of SI, where SI is calculated half-yearly and quarterly?
Re: Simple and Compound Interest
by Sreekant K - Tuesday, 22 October 2013, 10:19 PM
  http://courses.confederationc.on.ca/bm105/part3/unit9/bm9s3.html
Re: Simple and Compound Interest
by shantanu tyagi - Wednesday, 23 October 2013, 05:35 PM
  hello TG sir,

IN the question posted by Mohit
1) Some amount was lent on 6% per annum simple interest. After one year, Rs.6800 is repaid and the rest of the amount is repaid at 5% per annum. If the second year's interest is 11/20 of the first year's interest, find what amount of money was lent out.
a) 17000
b) 16800
c) 16500
d) 17500
e) None of these

It can be solved considering two situations.

Situation 1-
When the amount paid after 1 yr is deducted from Principal alone(no part of interest if deducted).Then the soln goes like

(x-6800)0.05=11/20(0.06x)
which gives x=20000 x is the amount lent.

Situation 2-
When the amount paid after 1 year is deducted from Principal and interest. The soln is

(1.06x-6800)=11/20(0.06x)
which gives x=17000

17000 is one of the options but again there is None of the above

Please throw Some light on the amount deduction to be done in this case.

Thanks
Re: Simple and Compound Interest
by Dhiman Bhattacharyya - Saturday, 7 December 2013, 10:22 PM
  Hi TG,

I have a doubt regarding this type of questions-

A sum of Rs 5775 is due to be repaid at the end of two years. If it has to be repaid in two equal annual instalments (the first instalment being paid at the beginning of the first year) at 10% per annum compounded annually, find the value of each instalment?

There is formula like P=x/(1+r/100)^2 + x/(1+r/100)

But also isn't another way to equate 5775=x(1.1) + x?

Please reply ASAP I am really bugged by this. sad
Re: Simple and Compound Interest
by TG team - Wednesday, 11 December 2013, 01:17 PM
  hi Dhimansmile

If the total amount to be repaid is 5775 and the questions says that the first of the two equal instalments is to be paid at the beginning of the first year, then the loan amount reduces to (5775 -X) where X is the instalment amount. And now, this remaining amount will grow @ 10% p.a. to reach a total of X again (Instalements are equal).

So     X =  (5775 - X) x (1.21)
2.21X=5775 x 1.21
X=3161.9
Hope i am clearsmile.


Re: Simple and Compound Interest
by Tushar Varshney - Sunday, 22 December 2013, 10:07 PM
  No Mr mohit u r not correct becoz this is simple interest not compound. I hope u understand
Re: Simple and Compound Interest
by Abhinav Chauhan - Saturday, 15 August 2015, 03:30 AM
  5775 is the total amount to be repaid at the end therefore amount borrowed should be less than 5775 and hence you cannot subtract x from 5775 at the begining.