stuck on a present value question...?

Update:

"today, brianna has 7424.83 in her bank account. for the last two years, her account has paid 6% compounded monthly. before then, her account paid 6% compounded semi annually, for four years. if she made only one deposit six years ago, determine the original principle."

please walk me through this. thanks!

5 Answers

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  • 1 year ago
    Favorite Answer

    The equation for compound interest is:

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

    Where A(t) is the amount at "t" years,

    P = initial principal (amount when t = 0)

    r = annual rate of interest

    n = number of times per year interest is calculated

    t = time in years

    We are told that today's balance is $7424.83 and was earning 6% for the last 2 years compounded monthly.

    So we can call A(2) = 7424.83, r = 0.06, n = 12.

    Using this we can solve for P for this stage, which will end up being the new A(4) for the second part:

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

    A(2) = P(1 + 0.06/12)^(12 * 2)

    7424.83 = P(1 + 0.005)²⁴

    7424.83 = P(1.005)²⁴

    7424.83 = P(1.127160)

    While I'm rounding here, I'm not rounding in my calculator to reduce errors due to rounding. One last step:

    P = 7424.83 / 1.127160

    P = 6587.20 (rounded to nearest penny)

    This was the starting balance when the account converted to monthly compounding. Now do this again with n = 2 and t = 4, we can solve for P to get the original deposit amount from 6 years ago:

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

    A(4) = P(1 + 0.06/2)^(2 * 4)

    6587.2 = P(1 + 0.03)⁸

    6587.2 = P(1.03)⁸

    6587.2 = P(1.26677)

    P = 6587.2 / 1.26677

    P = 5200.00 (rounded to nearest penny, rounded up from 5199.9965)

    So the starting deposit was $5200.

  • 1 year ago

    PV = FV / (1 + i)^n

    PV = 7424.83/(1+6%/12)^24/(1+6%/2)^8 = 5200.00

  • 1 year ago

    fyi ... do say 6% PER ANNUM compounded (time frame). < That is better English and better math.

    Source(s): accountant (degree and everything)
  • Mike G
    Lv 7
    1 year ago

    If A(t) = Present Value

    Ao = Initial Amount invested

    r = Annual Interest Rate

    n = number of compounding periods in 1 year

    t = number of years

    A(t) = Ao(1+r/[100n])^(nt)

    For the first 4 years

    A(4) = Ao(1+6/200)^8 = 1.26677Ao

    For the last 2 years

    A(2) = 1.26677Ao(1+6/1200)^24 = 1.42785Ao

    1.42785Ao = 7424.83

    Ao = 5199.999

    Ao = $5,200

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  • alex
    Lv 7
    1 year ago

    the original principle = x

    6% compounded semi annually, for four years --->x(1.03)^8

    6% compounded monthly , for four years --->[x(1.03)^8](1.005)^24

    [x(1.03)^8](1.005)^24 = 7424.83 --->x = $5200

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