Suppose you have a $$60,000$ loan with an annual percentage rate of $8\%$ for $25$ years.

a$.$ What are your required monthly payments?

b$.$ Suppose you pay off the loan in $15$ years, rather than $25.$ What are the required monthly payments?

c$.$ Explain why there are differences in the total amounts you pay over the loan terms for the two scenarios.

d$.$ What would be the effect of paying the required monthly rate and an additional $$100$ each month on the cost of the two loan?