Suppose you are a loan officer for a bank. A start-up company has qualified for a loan. You are pondering various proposals for repayment:

1. Lump sum of $250,000 five years hence. How much will you lend if your required rate of return is (a) 8%, compounded annually, and (b) 12%, compounded annually?

2. Repeat number 1, but assume that the interest rates are compounded semiannually.

3. Suppose the loan is to be paid in full by equal payments of $50,000 at the end of each of the next 5 years. How much will you lend if your required rate of return is (a) 8%, compounded annually, and (b) 12%, compounded annually?