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Interest problem

  • Thread starter Pinu7
  • Start date
  • #1
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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]t


This is getting a bit tough. Where do I go from here?
 
Last edited:

Answers and Replies

  • #2
378
2
Latex isn't working right now. It's bit hard to read.

But are you referring to a cash flow problem (annuities) i.e. there is a negative cash flow at t =0, and at the end of each year/month, there are equal positive cash flows.
http://www.zenwealth.com/BusinessFinanceOnline/TVM/Annuities.html


(it doesn't consider inflation)
 

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