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Math Help - Compound Interest

  1. #1
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    Compound Interest

    If Angela has $100 to invest at 10% per annum compounded monthly, how long will it be before she has $175? If the compounding is continuous, how long will it be?
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  2. #2
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    Quote Originally Posted by magentarita View Post
    If Angela has $100 to invest at 10% per annum compounded monthly, how long will it be before she has $175?
    The compound interest formula is:

    A = P\left(1 + \frac{r}{n}\right)^{nt}

    Where:
    • P = Principal amount (initial investment)
    • r = Annual interest rate (as a decimal)
    • n = Number of times the interest is compounded per year
    • t = Number of years
    • A = Amount after time t
    From the question, we can deduce that P=$100, r=0.1, n=12, t=?, A=$175 and hence inserting the values into the formula gives:

    175= 100\left(1 + \frac{0.1}{12}\right)^{12t}

    Now, solve for t and you will have the amount of years for the investment to grow from $100 to $175.
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  3. #3
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    Quote Originally Posted by magentarita View Post
    If Angela has $100 to invest at 10% per annum compounded monthly, how long will it be before she has $175? If the compounding is continuous, how long will it be?
    The continuous compound interest formula is:

    A = Pe^{rt}

    Where:
    • P = Principal amount (initial investment)
    • r = Annual interest rate (as a decimal)
    • t = Number of years
    • A = Amount after time t
    • e = Exponential function


    From the question, we can deduce that P=$100, r=0.1, t=?, A=$175 and hence inserting the values into the formula gives:

    175 = 100e^{0.1t}

    Now, solve for t and you will have the amount of years for the investment to grow from $100 to $175 with continuous compound interest.
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  4. #4
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    Great reply...

    Great reply as always!
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