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

Answer:

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  

Explanation:

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

$PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }$

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)

$PresentValue=\frac{6,700((1+0.06)^{15}-1) }{0.06(1+0.06)^{15} } =\frac{6,700(1.396558193)}{0.143793492} =65,072.07$

For b) is:

$PresentValue=\frac{6,700((1+0.06)^{40}-1) }{0.06(1+0.06)^{40} } =\frac{6,700(9.285717937)}{0.617143076} =100,810.19$

For c) is:

$PresentValue=\frac{6,700((1+0.06)^{75}-1) }{0.06(1+0.06)^{75} } =\frac{6,700(78.05692079)}{4.743415247} =110,254.18$

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

$PresentValue=\frac{A}{r}$

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

$PresentValue=\frac{6,700}{0.06}= 111,666.67$

Best of luck.