Thomas and Salom$$ plan to purchase $\frac{1}{2}$ home for $$279,000.$ They will pay $20\%$ down and finance the remainder for $15$ years at the APR of $3\mathrm{.}9\%,$ compounded monthly.

a$)$ How large are the monthly payments? $

b$)$ What will be their loan balance right after they have made their $36$th payment? $

c$)$ How much interest will they pay during the $3$rd year of the loan? $

d$)$ If they were to increase their montly payments by $$130,$ how long would it take to pay off the loan? Give your answer in whole months.