An investment offers $6,500 per year for 20 years, with the first payment occurr

Question

An investment offers $6,500 per year for 20 years, with the first payment occurring one year from now.

If the required return is 7 percent, what is the value of the investment? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What would the value be if the payments occurred for 45 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What would the value be if the payments occurred for 70 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What would the value be if the payments occurred forever? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

a) Net Present Value = 6500[(1/1.07)+(1/1.07)2+...+(1/1.07)20] is a finite Geometric Series with n = 20

= 6500[(1/1.07)20-1]/(1.07-1) = $ 68861.09

b) NPV = 6500[(1/1.07)+(1/1.07)2+...+(1/1.07)45] is a finite Geometric Series with n = 45
= 6500[(1/1.07)45-1]/(1.07-1) = $ 88435.89

c) NPV = 6500[(1/1.07)+(1/1.07)2+...+(1/1.07)70] is a finite Geometric Series with n = 70
= 6500[(1/1.07)70-1]/(1.07-1) = $ 92042.53

d) NPV = NPV = 6500[(1/1.07)+(1/1.07)2+...] is an infinite Geometric Series
= 6500/(1.07-1) = $ 92857.14

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