Question

An investment offers $6,700 per year for 15 years, with the first payment occurring one year from now. a. If the required return is 6 percent, what is the value of the investment today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $ b. What would the value today be if the payments occurred for 40 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $ c. What would the value today be if the payments occurred for 75 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $ d. What would the value today be if the payments occurred forever? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $

Answer 1

a.$65,072.07

b.$100,810.19

c.$110,254.18

d.$111,666.67

Step-by-step explanation:

a. The value of investment today if payment per year of $6,700 is made for 15 years is given as follows:

Present value today=R[(1-(1+i)^-n)/i]

Where

R=payment to made yearly=$6,700

i=interest per annum=6%

n=number of payments=15

Present value today=6,700[(1-(1+6%)^-15)/6%]=$65,072.07

b. The value of investment today if payment per year of $6,700 is made for 40 years is given as follows:

Present value today=6,700[(1-(1+6%)^-40)/6%]=$100,810.19

c. The value of investment today if payment per year of $6,700 is made for 75 year is given as follows:

Present value today=6,700[(1-(1+6%)^-75)/6%]=$110,254.18

d. The value of investment today if payment per year of $6,700 occurred forever

Present value today=P/i=6,700/6%=$111,666.67

where P=6,700, i=6%