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

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\[A _{n}=A _{n-1}(1.01)-400\]
An=An-1(1.01(-400
so my last equation was right?
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
I don't think my uni has any 1 credit hour class

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