Problem $4-15$

A lender is considering what terms to allow on a loan. Current market terms are $9$ percent interest for $25$ years for a fully amortizing

loan. The borrower, Rich, has requested a loan of $$106,000.$ The lender believes that extra credit analysis and careful loan control will

have to be exercised because Rich has never borrowed such a large sum before. In addition, the lender expects that market rates will

move upward very soon, perhaps even before the loan is closed. To be on the safe side, the lender decides to extend to Rich a CPM

loan commitment for $$100,700$ at $9$ percent interest for $25$ years; however, the lender wants to charge a loan origination fee to make

the mortgage loan yield $10$ percent.

Required:

a$.$ What origination fee should the lender charge?

b$.$ What fee should be charged if it is expected that the loan will be repaid after $10$ years?

Note: For all requirements, do not round intermediate calculations and round you final answers to the nearest whole dollar.

a$.$ Loan origination fee $-25$ year loan

b$.$ Loan origination fee $-10$ year loan