Algebra II

I'm pretty confused about these problems. We're learning growth and decay, but there are quite a few formulas.

1. Suppose $500 is invested at 6% annual interest compounded twice a year. When will the investment be worth $1000?

2. Suppose $500 is invested at 6% annual interest compounded continuously. When will the investment be worth $1000?

... I'm really confused

  1. 0
  2. 1
asked by Annie
  1. If the annual interest is 6 percent every half year the amount in the account is multiplied by 1.03 every half year.
    so after n half years the account will be worth:
    $500 * (1.03)* (1.03) * (1.03) etc n times
    or
    $500 * (1.03)^n
    so do the problem in half years
    $500 * (1.03)^n = 1000
    1.03^n = 2
    take the log of both sides remembering that log x^y = y log x
    n * .012837 = .301030
    n = 23.45 half years = 11.7 years
    -----------------------------------
    Now for the continuous problem you either have to know the formula from your text book or know calculus.
    Since I do not have a textbook, I will figure it out and find the formula
    dy/dt = .06 y
    dy/y = .06 dt
    ln y = .06 t + c
    y = e^(.06 t + c) = C e^.06 t
    when t = 0, y = $500 so
    THIS NEXT LINE IS PROBABLY IN YOUR TEXT
    y = 500 e^.06 t
    so we want
    1000 = 500 e^.06 t
    ln 2 = .06 t
    .693147 = .06 t
    so t = 11.55 years
    Just a little better than compounding twice a year

    1. 0
    posted by Damon
  2. By the way, a rule of thumb is that your money doubles in ten years at 7% interest.

    1. 0
    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra

    Determine if the equation y = 2^x represents exponential growth or decay I thought at first it was growth but now I think it might be decay because there is no "b" in a parentheses so do I assume b is less than 1 so it's decay?
  2. Math

    Does the function represent exponential growth or exponential decay. Identify the growth or decay factor. y=9 x (1/2) I'm not sure how to make the chart to show the decay.
  3. Math

    We are learning about linear and exponential growth and simple and compound interest. How do I know if I use .02 if my growth rate is 2% or if I use 1.02? What is the difference if I have the 1 in front? I'm a little confused
  4. Pre Algebra

    Im currently learning Exponential Growth and Decay and there is one problem that I don't understand... From this: 30/9, how do they get to this result: 3 1/3 ?
  5. Math+Growth/Decay

    3e^2x = G -3e^2x = G -3e^-2x = D 1/8e^2x = G -1/8e^-2x = D Would that be correct? I just made these examples up in my head. How can you tell if its growth or decay? I just look at the exponents. If is a negative then its decay? if
  6. Algebra

    Determine whether each function is an example of exponential growth or decay. Then find the y-intercept. a) y = 2(4)^x growth or decay y-intercept: b) y = 3(.25)^x growth or decay y-intercept:
  7. Algebra 1- Exponential Growth & Decay

    How are exponential growth and decay present in the real world? Give at least 2 examples for exponential growth and 2 examples of exponential decay. My Answer: I have only been able to think of one example of exponential growth
  8. algebra

    I'm really confused on substitution. My teacher has a terrible accent and cannot understand what she says. i get the basics myself but i'm pretty confused on the following problems: 1) y= 3x - 8 y= 4-x 2) 2x + 7y = 3 x=1- 4y 3) x
  9. Emergancy help!!!!!!!!!

    Classify the model as exponential growth or exponential decay. Identify the growth or decay factor and the percent increase or decrease per time period. y=16(1.25)^t
  10. Math

    How do I identify the initial value and the growth or decay for these problems? a) Q=25000 x (1/2)^t b) y=350 x 5* c) N=5000 x (9/10)^t

More Similar Questions