Question

An investment offers $5,700 per year, with the first payment occurring one year from now. The required return is 5 percent. b. a. What would the value be today if the payments occurred for 10 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) What would the value be today if the payments occurred for 35 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) What would the value be today if the payments occurred for 65 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) d. What would the value be today if the payments occurred forever? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value of 10 annual payments Present value of 35 annual payments Present value of 65 annual payments Present value of annual payments forever d.

Answer 1

The present value of the future payments can be calculated using the present value formula. The values would be $35,428.73 for 10 years, $95,930.05 for 35 years, $158,813.26 for 65 years, and $114,000 for payments occurring forever.

Step-by-step explanation:

To find the present value of future payments, we can use the present value formula:

Present Value = Payment / (1 + r)t

Where Payment is the annual payment, r is the required return as a decimal, and t is the number of years.

1. For 10 years:
   Payment = $5,700, r = 5% (0.05), t = 10 years
   Present Value = $5,700 / (1 + 0.05)10 = $35,428.73
2. For 35 years:
   Payment = $5,700, r = 5% (0.05), t = 35 years
   Present Value = $5,700 / (1 + 0.05)35 = $95,930.05
3. For 65 years:
   Payment = $5,700, r = 5% (0.05), t = 65 years
   Present Value = $5,700 / (1 + 0.05)65 = $158,813.26
4. For payments occurring forever:
   Payment = $5,700, r = 5% (0.05)
   Present Value = Payment / r = $5,700 / 0.05 = $114,000