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Calculus Solving for Present value of payments

  1. Apr 15, 2013 #1
    1. The problem statement, all variables and given/known data

    You value a car to be $30,000. If you plan to make continuous payments over 5 years and at an interest rate of r = :1.

    1) How much should you pay per year so that the present value of your total payments in 30; 000?
    2)What if instead you decided to let your payments increase with time and pay at a rate of $6000 + t1000 per year, where t is measured in years. How long would it take you to pay o the car ? (Note the equation you get might be dicult to solve, so you can use a graphing calculator to estimate.)


    2. Relevant equations

    The formula that i think i should use is

    PV = PMT(1-(1/(1+i)^n)) / i



    3. The attempt at a solution



    For part 1:

    solving for PMT I got 7913.48. Did i do that correctly?


    For part 2:
    Im not too sure how to approach this. Do i use the same equation and solve for t? I assume the t is the same as the n i used in my pv formula, is this correct?

    Thanks
     
  2. jcsd
  3. Apr 16, 2013 #2

    SteamKing

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    What does r = :1. mean? What does making 'continuous payments' mean?
     
  4. Apr 16, 2013 #3

    Ray Vickson

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    What does r = :1 mean? Do you mean to write r = 0.1? Is that the *annual* rate (that is, the interest rate is 10% per year)?

    Your formula is for discrete payments at regularly-spaced points in time, but the problem asked for a *continuous* stream of payments, and presumably using *continuous* compounding/discounting. That will turn an arithmetic/algebraic problem into a calculus problem! So, you need the formulas for continuous-time discounting.
     
  5. Apr 17, 2013 #4
    I'm pretty for q1 you need to use a continuous paying annuity formula which is [itex] PV=PMT*((1-v^n )/delta) [/itex] where [itex] delta=ln(1+r)[/itex] and [itex] v=1/(1+r) [/itex]
     
  6. Apr 17, 2013 #5

    Ray Vickson

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    I am 100% sure you should not use this formula.
     
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