Question $4\mathrm{.}16($page $111,$ the textbook$)$

A borrower is faced with choosing between two mortgage loans. Loan A is $$75,000,6\%$ mortgage rate for $30$ years, with $6$ discount points included in closing costs.

Loan B: the loan amount is $$75,000,$ mortgage rate is $7\%,2$ discount points will be charged.

The loan information can be listed as follows:

Loan A

Principal

Nonimal Interest Rate

Term

Points

Payment

Loan Balance after $20$ years

Loan Balance after $5$ years

$

Loan A

$6\mathrm{.}63\%$

Loan B

$?$

Loan B

$?$

$?$

a$)$ if the borrower will repay the loan after $20$ years, which loan has the lower effective interest rate?

b$)$ if the borrower will repay the loan after $5$ years, which loan has the lower effective interest rate?