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.