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Simple & Compound interest problems (Guru level)


sunilcyborg

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:hmm::2cents:I would like anyone to everyone to look into these problems & explain the solution:

 

:mad:1) A sum of Rs 550 was taken as a loan. This is to be paid back in two equal instalments. If the rate if interest be 20% compounded annually, then the value of each instalment is :

a) 421 b) 396 c) 360 d) 350

 

 

:2cents:2) The compound interest on a certain sum for 2 year is Rs 832 and simple interest is Rs 800. Find the sum and the rate percent

 

 

:hmm:3) The difference between the second and the third years interest in a certain sum at 5% compound interest is Rs 5.25. Find the sum.

 

 

4)A person borrows two equal sums at the same time at 5 and 4 percent respectively and finds that if he repays the former sum with simple interest on a certain date 6 months before the latter, he will hace to pay in each case the same amount, Rs 1100, Find the amount borrowed

 

a) Rs 850 b) Rs 1000 c) Rs 995 d) Rs 990

 

 

5) Find the effective annual rate corresponding to a nominal rate of 6 percent per anum, payable half-yearly

 

a) Rs 20.63 b) Rs 21.94 c) Rs 23.69 d) Rs 25

 

6) Which among the following two offers is a better one:

 

A) Investing an amount compounded annually at 1% per annum for 100 years

 

B) Investing the amount compounded annually at 100% per annum for 1 year

 

:idea: I am looking forward for the solutions

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Q1 :

The period of loan repayment is not mentioned. Assuming that the loan will be reurned in two years,

Compounded value after two years = 550(1 + 20/100)^2 = 792

Each instalment = 792/2 = 396

Hence B.

Q3:

Let a be the principal.

Second year's interest = a(1+1/20)^2 - a(1 + 1/20)

Third year's interest = a(1+1/20)^3 - a(1 + 1/20)^2

Difference = a(1+1/20)^3 - 2a(1 + 1/20)^2 + a(1 + 1/20)

= 21a/8000

So 21a/8000 = 5.25

a = 2000

So the sum is 2000.

 

Q6 :

A) Investing an amount compounded annually at 1% per annum for 100 years

(1 +.01)^100 = 2.7

B) Investing the amount compounded annually at 100% per annum for 1 year

(1 +1 ) = 2

So first option is better.

Q4 is not clear since it is not indicated that the other amount has been borrowed on simple or compound interest.

Q5 is also not clear because the interest rate should be in percentage but the options are in Rs.

:)

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Q1 :

The period of loan repayment is not mentioned. Assuming that the loan will be reurned in two years,

Compounded value after two years = 550(1 + 20/100)^2 = 792

Each instalment = 792/2 = 396

Hence B.

 

This is incorrect because the principal is reduced after the first payment. Here is how to solve it.

 

Let:

I1=interest paid in the first payment

I2=interest paid in the second payment

P1=principal paid in the first payment

P2=principal paid in the second payment

 

Because the payments are equal:

I1 + P1 = I2 + P2

 

Because all the principal is paid:

P1 + P2 = 550

 

First payment interest is on the full loan:

I1 = 550 x 0.2 = 110

 

Second payment interest is only on the remaining principal:

I2 = (550-P1) x 0.2

 

Substituting:

110 + P1 = (550 - P1)(0.2) + (550-P1)

110 + P1 = 110 - 0.2P1 + 550 - P1

2.2P1 = 550

P1 = 250

Payment = 250 + 110 = 360

 

Check:

P2 = 550 - P1 = 550 - 250 = 300

I2 = 0.2 x 300 = 60

Payment = 300 + 60 = 360

 

Paul

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:hmm::2cents:I would like anyone to everyone to look into these problems & explain the solution:

 

:mad:1) A sum of Rs 550 was taken as a loan. This is to be paid back in two equal instalments. If the rate if interest be 20% compounded annually, then the value of each instalment is :

a) 421 b) 396 c) 360 d) 350

Solution : C) back tracking : check for all ,

if take 421 then 1st yr 110 is interest => 311 Principal paid so remaining P = 550 - 311 = 239. so can be answer as (239)(1.2) not equal to 421.

if 360 then P paid 250 Rs. remaining P = 300 and 300 (1.2) =360 so answer.

:2cents:2) The compound interest on a certain sum for 2 year is Rs 832 and simple interest is Rs 800. Find the sum and the rate percent

Soluton: SI for one yr =400 , addition interest on 2nd yr = 32 rs. thus Interest on interest = 32 /400 = 8% now 8% of sum is 400 then sum is 5000.

 

:hmm:3) The difference between the second and the third years interest in a certain sum at 5% compound interest is Rs 5.25. Find the sum.

Solution:

3rd yrs = x{(1.05)^3 -(1.05)^2} = .055125 * x

2ndyr = x{(1.05)^2 -(1.05)} = .0525 * x

thus diff = .002625 x =5.25 => x =2000

4)A person borrows two equal sums at the same time at 5 and 4 percent respectively and finds that if he repays the former sum with simple interest on a certain date 6 months before the latter, he will hace to pay in each case the same amount, Rs 1100, Find the amount borrowed

 

a) Rs 850 b) Rs 1000 c) Rs 995 d) Rs 990

Solution:B

time is x then 5x =4(x+.5)

=> x = 2 thus 2 yr is the time for 5 %

check the amount using back tracking

sum is 1000

5) Find the effective annual rate corresponding to a nominal rate of 6 percent per anum, payable half-yearly

 

a) Rs 20.63 b) Rs 21.94 c) Rs 23.69 d) Rs 25

Solution:

Rate (1.03)2-1 =6.09% so Please check the options

6) Which among the following two offers is a better one:

 

A) Investing an amount compounded annually at 1% per annum for 100 years

 

B) Investing the amount compounded annually at 100% per annum for 1 year

Solution: A) as 100% for 100 yr using 1% simple interest and bcz it is compounded thus interest would be >100% so A) is better option.

No need for calculation.

:idea: I am looking forward for the solutions

Please check the comments

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Help Anyone! http://www.www.urch.com/forums/../images/smilies/rolleyes.gif

 

 

A watermelon weighs 5000gm, 99% of its weight is water. It is kept in a drying room and after some time it turns out that it is only 98% water by weight. What is its weight now?

 

1) 2500 gm

2) 4500 gm

3) 4950 gm

4) None of these

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1 more to go guys:tup:

 

A man borrows Rs 1200 in order to buy a new house and agrees to pay back a fixed sum of Rs 300 at the end of each subsequent year, If compound interest is charged at the rate of 5% per year, how much remains to be paid off at the end of fourth year?

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1 more to go guys:tup:

 

A man borrows Rs 1200 in order to buy a new house and agrees to pay back a fixed sum of Rs 300 at the end of each subsequent year, If compound interest is charged at the rate of 5% per year, how much remains to be paid off at the end of fourth year?

 

 

I waiting for your response guys

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Help Anyone! :rolleyes:

 

 

A watermelon weighs 5000gm, 99% of its weight is water. It is kept in a drying room and after some time it turns out that it is only 98% water by weight. What is its weight now?

 

1) 2500 gm

2) 4500 gm

3) 4950 gm

4) None of these

solution: answer is 1) 2500 gm

 

Explanation :

since when drying only the quantity of water will change but the pulp would remain same.

so initally 99% water : 4950 gm , 1% pulp = 50 gm because total weight is 5000gm

after drying 98% water = ? (we don't know the weight after drying)

2% pulp = 50 gm (as the weight of pulp would not change)

thus for calculating total weight we know that pulp is 2% and 50 gm thus 2% of what is equal to 50 gm

thus x*2/100 =50

=> x =2500 gm

NOTE: remember these are the problem related to base change in %. Later case we don't know the base.

so Always remember what is the base over what we want to calculate %.

 

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1 more to go guys:tup:

 

A man borrows Rs 1200 in order to buy a new house and agrees to pay back a fixed sum of Rs 300 at the end of each subsequent year, If compound interest is charged at the rate of 5% per year, how much remains to be paid off at the end of fourth year?

Solution:

Dear this is not a GMAT level question. so please don't put these type of questions.

 

Explanation:

 

1200

1) after one yr interest paid 1200 * .05= 60 Rs and Principal paid 300 - 60=240

thus P remaining = 1200 - 240 = 960

 

2)after 2nd yr interest paid 960*.05= 48 Rs and Principal paid =300 -48 = 252 thus P remaining = 960 - 252 = 708

 

3) after 3rd yr interest paid 708 * .05 = 35.40 Rs and Principal paid 300 - 35.40 =264.60 thus P remaining = 708 - 264.60 = 443.40

 

4)after 4th yr interest paid 443.40 * .05= 22.17 Rs and Principal paid 300 -22.17 = 277.83 thus

P remaining = 443.40 - 277.83 = 165.57 Rs

thus this is the amt he has to paid after 4th yr.

If you want to calculate the 5th installment then

that is 165.57 * (1.05) = 173.8485 Rs

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I wanted 2 add 1 more thing.. I knew the above problem had a tedious solution. I just thought may b I could find a shorter method to solve it.

Dear,

Base change questions always come in GMAT , so be familiar with these question. they are tricky and have traps.

But in case of SI and CI very simple questions come so don't need to go for higher level of interest based question

:)

 

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