Chapter 2.4, Problem 59AYU

Mortgage Fees Fannie Mae charges a loan-level price adjustment (LLPA) on all mortgages, which represents a fee homebuyers seeking a loan must pay. The rate paid depends on the credit score of the borrower, the amount borrowed, and the loan-to-value (LTV) ratio. The LTV ratio is the ratio of amount borrowed to appraised value of the home. For example, a homebuyer who wishes to borrow $\$250,000$ with a credit score of 730 and an LTV ratio of $80\%$ will pay $0.75\%\left(0.0075\right)$ of $\$250,000,$ or $\$1875.$ The table shows the LLPA for various credit scores and an LTV ratio of $80\%$.

$\begin{array}{cc}\text{Credit}\text{Score}& \begin{array}{l}\text{Loan-Level}\\ \text{Price}\text{Adjustment}\text{Rent}\end{array}\\ \le 659& 3.00\%\\ 660-679& 2.75\%\\ 680-699& 1.75\%\\ 700-719& 1.25\%\\ 720-739& 0.75\%\\ \ge 740& 0.50\%\end{array}$

Construct a function $C=C(s),$ where $C$ is the loan-level price adjustment (LLPA) and $s$ is the credit score of an individual who wishes to borrow $\$300,000$ with an $80\%$ LTV ratio.

What is the LLPA on a $\$300,000$ loan with an 80% LTV ratio for a borrower whose credit score is $725?$

What is the LLPA on a $\$300,000$ loan with an 80% LTV ratio for a borrower whose credit score is $670?$