223.2

2. A friend wants to borrow $100 from you. She promises to pay you back $115 in two years.

1. What annual interest rate is she offering you? (4 pts.)

   \( 100 = \frac{115}{(1+r)^2} \) , so \( r = 0.07238 \)

2. If you have a bank account that pays 5%, compounded quarterly, is the loan a good deal for you (assume that you can be sure that she will pay you back)? (4 pts.)

First you must find the effective annual rate for the bank's offer:

\( \left ( 1 + \frac{.05}{4} \right )^4 = 1.0509 \) or \( 5.09 \% \)

so loaning to your friend offers a higher rate of return.

3. If you expect inflation to be 3% per year (annual compounding), what real rates of return are you earning on the loan and your bank account? (6 pts.)

\( \frac{1.07238}{1.03} = 1.041146 \) and \( \frac{1.0509}{1.03} = 1.020291 \) , so you're earning 4.11% and 2.03%.

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