Algebra II

posted by Annie

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. Damon

    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

  2. Damon

    By the way, a rule of thumb is that your money doubles in ten years at 7% interest.

Respond to this Question

First Name

Your Answer

Similar Questions

  1. math/algebra

    Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1+r/2)^2represents the value of the investment after 1 year. Rewrite this expression …
  2. College Algebra

    Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1+r/2)^2 represents the value of the investment after 1 year. Rewrite this expression …
  3. Finance

    . (TCO 3) Mark deposited $1,000 today, in an account that pays eight percent interest, compounded semi-annually. Which one of the following statements is correct concerning this investment?
  4. math

    Suppose that you have $12,500 to invest over a 4 year period. There are two accounts to choose from: 4.5% compounded monthly or 4.3% compounded continuously. a. Write the formula for the first account’s compound interest for n compounding …
  5. algebra

    Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial represents the value of the investment after 1 year. Rewrite this expression without …
  6. algebra

    An investment adviser invested $14,000 in two accounts. One investment earned 4% annual simple interest, and the other investment earned 2.5% annual simple interest. The amount of interest earned for 1 year was $458. How much was invested …
  7. Still confused

    An investment adviser invested $14,000 in two accounts. One investment earned 4% annual simple interest, and the other investment earned 2.5% annual simple interest. The amount of interest earned for 1 year was $458. How much was invested …
  8. college algebra

    An investment initially worth $5300 earns 7.7% annual interest, and an investment initially worth $8000 earns 5.6% annual interest, both compounded annually. How long will it take for the smaller investment to catch up with the larger …
  9. Algebra 1

    1.the number of bacteria present in a colony is 180 at 12 noon and the bacteria grows at a rate of 22% per hour. how many will be present at 8pm?
  10. college algebra

    I'm completely drawing a blank on how to do this. A woman has $500,000 invested into two real estate properties. One yields an annual return on 12% and the other returns 15% per year on her investment. Her total annual return from …

More Similar Questions