How long does it take for an investment to quadruple in value if it is invested at 11% compounded continuously? Type the exact

Question

How long does it take for an investment to quadruple in value if it is invested at 11% compounded
continuously? Type the exact answer as your answer (no decimal approximations).

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Thu Giang 2 weeks 2021-08-30T01:39:17+00:00 1 Answers 0 views 0

Answers ( )

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    2021-08-30T01:40:43+00:00

    Let’s assume we have $100 and an interest rate of 7%. For the $100 to quadruple it means that the future value would be $400. Thus, because we are talking about compounding daily we will set us the equation as follows:

    100 * (1+1.07)x = 400

    Then we will take 400 and divide it by 100 getting:

    1.07X = 4

    Now we have encountered a problem where we do not know exponent, so we will use logarithm to calculate such and transform our equation to: Log1.07(4)=X

    Using our calculator we will find that it takes about 20.4895 days to quadruple the money invested under 7% interest rate compounded daily.

    2nd: Using the same $100 but with the rate of 5.5% compounded continuously we will be using A=PERT formula

    where:

    P (principal) is equal to hypothetical $100

    E (e) is a mathematical constant, which is approximately 2.718

    R (rate) is the interest rate, in our case it is 5.5%

    T (time) is the time required for money to grow

    A (amount) is the final amount desired, which is 4 times larger of $100, thus $400

    We have the following:

    400 = 100 * e0.055t

    400/100 = e0.055t

    4 = e0.055t

    Then we will apply natural log to both sides of the equations and get the following:

    ln(4) = ln(e0.055t)

    Since e is the base of ln(x) the equation simplifies to:

    ln(4) = 0.055t

    Using the calculator to find ln(4) we are getting:

    1.38629 = 0.055t

    Lastly find t

    t = 1.38629/0.055

    t = 25.20535202

    Plug the answers back to the original equation to verify the answers.

    1st part of the question answer: t = 20.4895

    2nd part of the question answer: t = 25.20535202

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