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Thread: Simple & Compound interest problems (Guru level)

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    Eager! sunilcyborg's Avatar
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    Simple & Compound interest problems (Guru level)

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

    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


    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


    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

    I am looking forward for the solutions

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    2) x(1+r)^2-x=832...............eq 1
    x2r=800..................... eq 2


    eq1- eq2 gives xr^2=32 or x=32/r^2
    substitute x value in eqn 2

    32*2*r/r^2=800
    or r =64/800 or 8%

    Again putting 8% in eqn 2 we can determine X

    x*2*0.08=800
    or x=5000

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    3. x[(1.05)^3-1]-x[(1.05)^2-1]= 5.25
    x[1.05^3-1.05^2]=5.25
    x*1.05*.05=5
    or x = 95

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    Thanks a lot for the help.. The answer for Question 3) is Rs 2000

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    An Urch Guru Pundit Swami Sage 12rk34's Avatar
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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.
    Last edited by 12rk34; 03-19-2009 at 11:04 AM.

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    Quote Originally Posted by 12rk34 View Post
    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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    Quote Originally Posted by 12rk34 View Post
    Q1 :

    Q6 :
    A) Investing an amount compounded annually at 1% per annum for 100 years
    (1 +.01)^100 = 2.7
    (1 +.01)^100 = 2.7 ? (How do we get this )

    Thanks

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    An Urch Guru Pundit Swami Sage 12rk34's Avatar
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    Quote Originally Posted by ACETARGET View Post
    (1 +.01)^100 = 2.7 ? (How do we get this )

    Thanks
    Use calculator.

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    GMAT TEST EXPERTS MBAchase's Avatar
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    Quote Originally Posted by sunilcyborg View Post
    I would like anyone to everyone to look into these problems & explain the solution:

    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.

    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.

    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.
    I am looking forward for the solutions
    Please check the comments

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    Eager! sunilcyborg's Avatar
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    Thanks a lot guys.

    Paul your explanation is perfect. The answer for 1) is Rs 360.


    There is 1 more solution for the same

    Let the value of each instalment be x

    (x/(1+(20/100)) + (x/(1+(20/100)))2 = 550

    5x/6 + 25x/36 = 550 x=360

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