Problem 0.14

This isn't really a problem computational theory. But I will complete this anyway.

Define x to be the monthly payment. r to be the monthly interest rate, T be the number of months.

Total future value of these payment is

$ \sum\limits_{i = 0}^{T-1}{x(1+r)^{i}} = x\frac{(1+r)^n - 1}{(1 + r - 1)} = x\frac{(1+r)^n - 1}{r} $

But then it must equals to the future value of the loan, so we have

$ x\frac{(1+r)^n - 1}{r} = p(1+r)^n $

Plugging in the values it is easy to see the answer is $536.82.