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Math Help - logarigthm word problems

  1. #1
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    logarigthm word problems

    i think im supposed to use logarigthms. i have no idea where to even start with this.
    4. You have $380,000 in your bank account. The interest rate in your account is 5%. Solve for the following:

    a. How much interest will you accumulate if interest is compounded annually over the next five years?

    b. How much interest will you earn in your account over the next five years with continuous compounding? You can use a scientific calculator or the =Exp() function in Microsoft Excel. If you are crafty you can also find web pages that will do the calculations for you. Regardless, show your steps and your work.
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  2. #2
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    Quote Originally Posted by brandilee View Post
    4. You have $380,000 in your bank account. The interest rate in your account is 5%. Solve for the following:

    a. How much interest will you accumulate if interest is compounded annually over the next five years?

    b. How much interest will you earn in your account over the next five years with continuous compounding?...
    Hello,

    to a. :

    If A(0) is the initial account, A(t) is the the account after t years and i is the interest rate then you have:

    A(t) = A(0) \cdot (1+i)^t . Plug in the given values:

    A(5) = 380000 \cdot \left(1+\frac i{100}\right)^5 \approx 484986.99

    to b. :

    Continuous compounding is calculated by:

    A(t)=A(0) \cdot e^{\frac{i \cdot t}{100}} . Plug in the given values:

    A(5) = 380000 \cdot e^{0.05 \cdot 5} \approx 487929.66
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