With the interest rates are going down, you have decided to buy this beautiful $3-$year old townhome in Madison, AL for $$340,000,$ and you are qualified to apply for an FHA loan where you are supposed to put $3\mathrm{.}5\%$ down. The loan officer of the mortgage company is offering you two options:

Option $1$: Get a $4\mathrm{.}8\%$ APR for a $30-$year term.

Option$-2$: Assume the current owner$$s$/$seller$$s mortgage that has an interest rate of $6\%$ APR, a remaining terms of $27$ years $($the original term was $30$ years$),$ a remaining balance of $$270,000$ and payments of $$1,400$ and obtain a second mortgage for the remainder balance of $$58,100$ at $7\mathrm{.}2\%$ with a $10-$year repayment term.

What is the effective interest rate for Option$-2?(10$ pts$.)$

Compute the monthly mortgage payments for both options. $(10$ pts$.)$

Compute the total of the interest payments for both options. $(10$ pts$.)$

What interest rate makes the two options equal to each other? $(10$ pts$.)$