Chapter 2.4, Problem 59AE

Mortgage Fees Fannie Mae charges a loan-level price adjustment (LLPA) on all mortgages, which represents a fee 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 $\text{\$250,000}$ with a credit score of 730 and an LTV ratio of $\text{80\%}$ will pay $0.5\%\left(0.005\right)$ of $\$250,000$, or $\$1250$. The table shows the LLPA for various credit scores and an LTV ratio of $80\%$.

(a) Construct a function $C=C\left(s\right)$, 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.

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

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