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.

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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.

Mathematics
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discrete mathmatics.... thats a higher level college course.
An=An−1(1.01)−400
so now balance = past balance(1.01) - 400 ?

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\[A _{n}=A _{n-1}(1.01)-400\]
yes
A0 = 10000 the first payment is 10000(1.01) + 400 B[n]=B{n-1}... balance due right?
yes
went wrong way should be adding bc of debt
B{n-1} - B{n-1}(.01) - 400 = B{n} B{n-1}(1-.01) - 400 = B{n} then right?
how does that look?
We want the balance or the payments?
makes sense
required payments
the payments are: B{n}(1.01) + 400; right? or you say to negate them to account for debt?
yes
-(1.01)B{n} - 400 = B{n+1} then maybe?
ok how about this For the following affine discrete dynamical systems: a. un=un-1-2 where u0=4 b. un=un-1+3 where u0=1 the value of r is 1, so the solution formulas given in this lesson do not apply. i. Use iteration (by hand or with your calculator) to explore the first few terms of each sequence. ii. On the basis of (i), conjecture a formula for a solution u(n) of the general affine system with r=1: (I) u0=c (R) un=un-1+d for n > 0
I have the tables
If I have \[u _{n}=u _{n-1}+d\]
u0=4

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