Problem $3$

$$ Loan $1$: $$200,000$ at $4\mathrm{.}5\%$ for $30$ years, monthly payments, and no origination cost. APR $=4\mathrm{.}80\%$

$$ Loan $2$: $$200,000$ at $4\mathrm{.}25\%$ for $30$ years, monthly payments, and no origination cost.

Question

$1.$ What is the discount point charged on Loan $1$ assuming there is no cost associated with the origination?

$$6,853\mathrm{.}91$

$2.$ How many points must be charged on the $2$nd loan to equalize the APR on the two loans?