One year ago, Stan borrowed 10,000 from Susan and agreed to pay the entire amount today. He offers to pay 5,000 now and 5,500 in one year. If Susan's required rate of return is eight percent, the total value today of these two payments is:

One year ago, Stan borrowed 10,000 from Susan and agreed to pay the entire amount today. He offers to pay 5,000 now and 5,500 in one year. If Susan's required rate of return is eight percent, the total value today of these two payments is:

• A. 9,000
• B. 10,500
• C. 10,093
• D. 11,000

Answer: (C)

The concept here is time value of money: the value today of future cash is found by discounting at the required rate of return. The payment made today has a present value equal to itself, so 5,000. The payment to be made in one year is worth 5,500 today divided by 1.08, which is 5,500 / 1.08 ≈ 5,092.59. Adding these together gives 5,000 + 5,092.59 ≈ 10,092.59, which rounds to 10,093. So the total value today of the two payments is approximately 10,093.

The concept here is time value of money: the value today of future cash is found by discounting at the required rate of return. The payment made today has a present value equal to itself, so 5,000. The payment to be made in one year is worth 5,500 today divided by 1.08, which is 5,500 / 1.08 ≈ 5,092.59. Adding these together gives 5,000 + 5,092.59 ≈ 10,092.59, which rounds to 10,093. So the total value today of the two payments is approximately 10,093.