A lender is considering what terms to allow on a loan. Current market terms are 8 percent interest for 25 years for a fully amortizing loan. The borrower, Rich, has requested a $100,000 loan. 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 Rich a fixed rate, constant payment mortgage (CPM) loan commitment of $95,000 at 9 percent interest for 25 years. However, the lender wants to charge a loan origination fee to make the mortgage loan yield 10%. What origination fee should the lender charge? What fee should be charged if it is expected that the loan will be repaid after 10 years?

1. The origination fee that the lender should charge if Rich will repay the loan after 25 years = $20,000 approximately.

2. The origination fee that the lender should charge if Rich will repay the loan after 10 years = $6,600 approximately.

Explanation:

a) Data and Calculations:

Amount requested by Rich = $100,000

Amount the bank is willing to lend Rich = $95,000

Interest rate = 9%

Period of loan = 25 years or 10 years

From an online finance calculator:

At 10% interest rate:

PMT = $-10,465.97

Sum of all periodic payments = $-261,649.17

Total Interest = $166,649.17

At 9% interest rate:

PMT = $-9,671.59

Sum of all periodic payments = $-241,789.84

Total Interest = $146,789.84

Expected Origination Fee:

Interest at 10% = $166,649.17

Interest at 9% =  $146,789.84

Required origination fee = $19,859.32 ($166,649.17 - $146,789.84)

This is equivalent to $20,000

Payment after 10 years:

At 10% interest rate:

PMT = $-15,460.81

Sum of all periodic payments = $-154,608.13

Total Interest = $59,608.13

At 9% interest rate:

PMT = $-14,802.91

Sum of all periodic payments = $-148,029.09

Total Interest = $53,029.09

Expected Origination Fee:

Interest at 10% = $59,608.13

Interest at 9% =  $53,029.09

Required origination fee = $6,579.04 or $6,600 ($59,608.13 - $53,029.09)