Use the mathematical models for linear equations to solve the given problem:

A loan of $$200,000$ is taken out over $20$ years at an annual interest rate of $4\%.$ Compute the $($constant$)$

loan repayment rate and the total interest paid. Also, find out how much sooner the loan would be

repaid and what savings in interest would be achieved if the loan repayment rate were increased by

one half from the start.