Question

Assume a discount rate of 10.0% per year. Using the concept of discount factors to compare receiving $20 today (T=0) to receiving $20 20 years from now (T=20). Which of the following statements is the most accurate:

1. The $20 received 20 years from now is worth only 5% of the value today

2. The $20 received 20 years from now is worth only 10% of the value today

3. The $20 received 20 years from now is worth only 15% of the value today

4. The $20 received 20 years from now is worth only $4 today

5. The $20 received 20 years from now is worth only $6 today

Answer 1

Answer:

Correct answer is:

The $20 received 20 years from now is worth only 15% of the value today

Explanation:

Discount rate =10%

Periods = 20 years

Future value = $20

Present value (PV) = FV / (1 + Discount rate) ^{Number of periods}

= $20 / (1 + 10%) ²⁰

= $2.97287

The PV as %age of FV = $2.97287 / $20 = 14.864% or 15% (rounded off)

This means $20 received 20 years from now is worth only 15% of the value today

Hence option C is most accurate and other options A, B, D and E are incorrect.