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Pinu7
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Homework Statement
This is not a problem in my calculus book.However, I am sure this involves calculus. This is also not a question from an economics class, it is just curiosity.
My question is: If I have a debt that is continually compounded, and I continually pay off the debt at a constant rate, how long will it take to pay off the debt?
Homework Equations
Compund interest(PERT)
The Attempt at a Solution
Let:
r=rate on the debt. (assume annually)
y= amount of money I will pay per year.
[tex]\Delta[/tex]t= an increment of time of which I will pay a quanta of money.
During the time [tex]\Delta[/tex] t since I started the debt, I will owe er[tex]\Delta[/tex]t
At this point I will pay my first quanta of money which would be y[tex]\Deltat[/tex]. and w
Right before I make my second payment on time 2[tex]\Delta[/tex]t, I will owe the money f
money owed from last increment AND the compound interest since that time.
ie I will owe (et[tex]\Delta[/tex]t-y[tex]\Delta[/tex]t)er[tex]\Delta[/tex]t=e2r[tex]\Delta[/tex]t-y[tex]\Delta[/tex]te[tex]\Delta[/tex]t
Continuing the pattern, the money I would owe right before my nth payment is:
en[tex]\Delta[/tex]t-y[tex]\Delta[/tex]te(n-1)[tex]\Delta[/tex]tThis is getting a bit tough. Where do I go from here?
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