Question

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

Answer 1

Ans.

a) The value today if the payments occured for 15 years would be:$65,072.07

b) The value today if the payments occured for 40 years would be: $100,810.19

c) The value today if the payments occured for 75 years would be: $110,254.18

d) The value today if the payments occured forever would be: $111,666.67

Step-by-step explanation:

Hi, except for c) (we´ll talk about later about c.) the equation that we need to use is:

`PresentValue=(A((1+r)^(n)-1) )/(r(1+r)^(n) )`

Where:

A = Annuity (yearly payment, in our case $6,700)

r = Discount rate (in our case 6% or 0.06 for the formula)

n = Period of time (for a) is 15, b) is 40, c) is 75)

So, let´s solve a)

`PresentValue=(6,700((1+0.06)^(15)-1) )/(0.06(1+0.06)^(15) ) =(6,700(1.396558193))/(0.143793492) =65,072.07`

For b) is:

`PresentValue=(6,700((1+0.06)^(40)-1) )/(0.06(1+0.06)^(40) ) =(6,700(9.285717937))/(0.617143076) =100,810.19`

For c) is:

`PresentValue=(6,700((1+0.06)^(75)-1) )/(0.06(1+0.06)^(75) ) =(6,700(78.05692079))/(4.743415247) =110,254.18`

Finally, for d) which is if the payments were made forever, the formula would be:

`PresentValue=(A)/(r)`

So the present value if this payments were made forever would be:

`PresentValue=(6,700)/(0.06)= 111,666.67`

Best of luck.