A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

A debt of $10,000 is to be amortized by equal payments of $400 at the end of each month, plus a final payment after the last $400 payment is made. If the interest is at the rate of 1% compounded monthly (the same as an annual rate of 12% compounded monthly), i. Write a discrete dynamical system that models the situation. ii. Construct a table showing the amortization schedule for the required payments. iii. Find a solution for the system.

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[A _{n}=A _{n-1}(1.01)-400\]

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is that correct?

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or \[A _{n}=10000(1.01)^{n-1}-400\]

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[A _{n}=A _{n-1}(1.01)-400\]

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    An=An-1(1.01(-400

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so my last equation was right?

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Here is how I would solve P-Principle D-Monthly Payment R-(Monthly interest rate) 1st Month - P(1+R)-D 2nd Month - [P(1+R)-D][(1+R)]-D =\[P(1+R)^2 - D(1+R)-D=P(1+R)^2 - D(1+(1+R))\] 3rd Month \[P(1+R)3−D(1+(1+R)+(1+R)^2)\] Nth Month - \[P(1+R)N−D(1+(1+R)+(1+R)^2+.....+(1+R)^{N-1})\] \[(1+(1+R)+(1+R)^2+.....+(1+R)^{N-1})\] is a gemotric series Formula For Sum of Geomtric Series \[\sum_{0}^{N}v^n={( 1-v^{n+1})} /(1-v)\] our equation is : \[P(1+R)^N-D\left(-\frac{1-(1+R)^N}{R}\right)\] Simplified to \[\frac{D \left(1-(R+1)^N\right)}{R}+P (R+1)^N\] For this particular problem: \[\frac{400\left(1-(1.01)^N\right)}{.01}+10000(1.01)^N=0\] N=28.91 Month

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't think my uni has any 1 credit hour class

  9. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.