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Compound Interest

  1. Oct 17, 2017 #1
    1. The problem statement, all variables and given/known data

    Amy deposited $1000 into an account that earns 8% annual interest compounded every 6 months. Bod deposited $1000 into an account that earns 8% annual interest compounded quarterly. If neither Amy nor Bob makes any additional deposits or withdrawals in 6 months, how much more money will Bob have in his account than Amy?



    2. Relevant equations

    A = P(1+r/n)^nt

    3. The attempt at a solution
    For Ammy

    P=1000, t=1( annual), n=2 (compounded 6 months), r=8%=0.08
    A= 1000(1+0.08/2)^2= 1000(1.04)^2=1.0816= 1081.6

    Kindly tell why is the solution wrong?

    Zulfi.
     
  2. jcsd
  3. Oct 17, 2017 #2

    phyzguy

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    You calculated how much money Amy will have after 1 year. The problem says, "in 6 months, how much more money will Bob have in his account than Amy?"
     
  4. Oct 17, 2017 #3
    Hi,
    I am to find correct value for Ammy:

    P=1000, t=1( annual), n=1 (compounded 6 months and we are calculating only for the 1st period not the whole year), r=8%=0.08
    A= 1000(1+0.08/2)^2= 1000(1.04)^1=1040
    This is correct.
    For Bob:


    P=1000, n=2(compounded quarterly , so 4 times but we have to calculate for 6 months so n=2, r=0.08, t=1

    Now A = P (1 + r/n)^ (nt)

    A= 1000(1 + 0.08/2)^(2*1)
    This is giving a wrong answer. Some body please guide me

    Zulfi.
     
  5. Oct 17, 2017 #4

    phyzguy

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    Amy looks correct now. For Bob, it should be (1 + 0.08/4)^2.
     
  6. Oct 17, 2017 #5

    SammyS

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    In your relevant equation section, What value should you use for t in both cases ?

    A = P(1+r/n)nt
    .
     
    Last edited: Oct 20, 2017
  7. Oct 17, 2017 #6
    Hi,
    I have used t=1 in both the cases, because it says "annual interest". I cant understand why n=4 in Bob case. It says quarterly so its 4 ( periods of interest of 3 months) but for 6 months we should have n=2 because there are 2 periods of 3 months.

    Some body please guide me.

    Zulfi.
     
  8. Oct 18, 2017 #7

    phyzguy

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    If you get 8% interest per year, you only get 2% in 3 months, not 4%.
     
  9. Oct 20, 2017 #8

    SammyS

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    t is the number of years. The question asks ".. in 6 months, how much more money will Bob have in his account than Amy?"

    I'm pretty sure that 6 months is 1/2 year rather than i year, so t = 0.5, in both cases.
     
  10. Oct 21, 2017 #9
    Hi,
    Thanks. I have solved this problem.
    For Amy:

    A = the amount of money that Ammy has after 6 months, because the problem asks how much he has after 6 months.=?
    P = the original amount of money that Amy invested (principal) -1000
    r = the annual interest rate = ?? (that is a 12 month rate) =0.08
    n = the number of times that interest is compounded per year = 2
    t = the number of years the money is invested =.5A = P (1 + r/n)^ (nt)
    A= 1000(1+0.08/2)^(2 *1/2)
    A= 1000(1+0.04) ^1 = 1000 (1.04) = 1040

    For Bob:
    A = the amount of money that Bob has after 6 months, because the problem asks how much he has after 6 months.=?
    P = the original amount of money that Amy invested (principal) -1000
    r = the annual interest rate = ?? (that is a 12 month rate) =0.08
    n = the number of times that interest is compounded per year = 4
    t = the number of years the money is invested =.5
    A = P (1 + r/n)^ (nt)
    A= 1000(1+0.08/4)^(4*1/2) = 1000(1+0.02)^2 = 1000(1.02)^2 = 1.0404=1040.4
    I think I am right this time.

    Now difference =A=1040.4-1040=0.4

    Zulfi.
    Zulfi.
     
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