Post a New Question

Calculus

posted by .

If you invest $5000 in a stock that is increasing in value at the rate of 12% per year, then the value of your stock is given by:

f(x) = 5000(1.12)^x, where x is measured in years

a) find average value from x = 2 to x = 3
b) find instantaneous value at x = 3


a) f(x) = 5000(1.12)^{5 - 2} = 5000(1.12)^3 = 7024.64
b) f'(x) = (5000(1.12)^3)(ln 1.12) = (7024.64)(0.113) = 796.093


Did I do the questions correctly?

  • Calculus -

    average = integral over x from x1 to x2 / (x2-x1)
    = 5000 int 1.12^x dx from 2 to 3 over 1
    int 1.12^x dx = 1.12^x/ln 1.12
    ln 1.12 = .1133
    1.12^3 = 1.405
    1.12^2 = 1.254
    (1.405 - 1.254)/.1133 = 1.333
    5000 *1.333 = 6663.72

    b
    f(3) = 5000*1.12^3 = 7024.64

    note in part a it is an exponential not a sequence. The value is increasing constantly (presumably) not in quarterly or yearly jumps as in with compound interest in most banks.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    I am confused on how to solve this problem : $5000 is invested for 4 years at 7% per annum compound interest. a. what will the amount be at the end of this period?
  2. Math

    Purchased $10,000 in stock, invested $5000 of own money, borrowed remaining $5000 at 8% interest. Stock increases by 10%, what is the rate of the investor's return?
  3. value of common stock

    • Emerson Electric common stock that is selling for $80 with a par value of $5. This stock recently paid a $2.10 dividend, and the firm’s earnings per share have increased from $2.40 to $4.48 in the past 5 years. An equivalent …
  4. Finance

    Hooks Athletics, Inc., has outstanding a preferred stock with a par value of $30 that pays a dividend of $2.50. The preferred stock is redeemable at the option of the stockholder in 10 years at a price equal to $30. The stock may be …
  5. Finance

    Sports Novelties, Inc., has experienced an explosion in demand for its feathered football novelties. The firm currently (time 0) pays a dividend of $0.25 per share. This dividend is expected to increase to $0.75 per share 1 year from …
  6. Finance

    Emerson Electric common stock is selling for $36.75. par value is $5. stock recently paid $1.32 in dividend and the firm's earnings per share increased from $1.49 to $3.06 in the past 5 years. The firm expects to grow at the same rate …
  7. calculus - please help!

    If two resistors R1 and R2 are connected in parallel, then the total resistance R measured in ohms is given by 1/R=1/R1+1/R2 If the resistance of R1 and R2 are increasing at 330 and 660 ohms per second respectively, then the rate of …
  8. College Algebra

    Tina invested $30,000 in a stock. In the first year, the stock increased in value by 10%. In the second year, the stock decreased in value by 20%. What percentage gain is requird in the third year for Tina's stock to return to its …
  9. MATH

    AN INVESTMENT OF $5000 IN THE STOCKMARKET WITH THE VALUE INCREASED BY 13% WILL EARN $650 FROM THE VALUE OF THE STOCK ($5000 x0.13) the new value would be $5650($5000 PLUS $650)
  10. Algebra

    Larry invested a total of $5000 in three stocks during the first year the first stock increasing value by 8% the second stock increase by 6% and the third stock increase by 1% in the first year he earn a profit $310 if Larry invested …

More Similar Questions

Post a New Question