# Here’s another way to look at it. suppose you want to borrow

Here’s another way to look at it. Suppose you want to borrow \$100,000. You choose a 30-year fixed rate loan at 7.5%, and pay one discount point (\$1,000), a 1% origination fee (\$1,000), and \$350 in other fees. Although the lender is giving you a loan for \$100,000, you have paid \$2,350 to the lender. Your payments are based on a loan of \$100,000, but your net proceeds are only \$97,650. Hence your APR is 7.75%. In other words, if you selected a rate of 7.75% and did NOT pay the discount point, the origination fee, or the \$350 in other fees, the APR says you would have the same overall value as the 7.5% loan with the \$2,350 in expenses.

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There are substantial limitations to the APR. In the previous example it was noted that the two loans (7.5% with \$2,350 in expenses and the 7.75% with no expenses) were the same value with respect to the APR. However, the APR assumes both loans go to the full term. If the loan is paid off in five to seven years (the average life of a mortgage), the two loans are NOT the same value. The higher-rate loan is the better value. Suppose the borrower with the 7.5% loan sells the house in five years. That borrower has made 60 payments of \$694.87 plus the initial expenses (\$2,350) for a total of \$44,042.20. The borrower with the 7.75% loan has made sixty payments of \$711.82 with no initial expenses for a total of \$42,709.20. The higher-rate loan costs \$1,333 LESS than the lower rate loan. Clearly, in this case using APR to make a decision would be unwise. There are similar cases when a loan with the lower APR may actually cost the borrower more when all factors are considered.

1. In paragraph 1: Calculate:

 The monthly payments on the mortgage

 The monthly IRR (use PMT )

 Show that the APR in the paragraph = monthly IRR * 12

 Compute the EAIR

2. In paragraph 2:

 Compute the monthly IRR, APR and EAIR for both loans (word of warning: the numbers on the Web page are slightly off).

 Which loan is preferable?

3. The Web page claims that loan 2 is preferable because the total payments over 60 months on this loan are lower than that on loan 1. Show that this is wrong.

4. Despite its higher initial cost, you might think that loan 2 is preferable because it has a higher initial loan amount. Calculate how much you would need to borrow with loan 1 in order to receive a net amount of \$100,000 (you can do this calculation using Goal Seek, but it can also be done using the formulas of Chapter 2). Doing it this way, show that Loan 1 is preferable.

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