An engineer estimates that the annual toll revenue from a newly proposed highway

Question

An engineer estimates that the annual toll revenue from a newly proposed highway construction over 20 years will increase at a rate of 4%. The revenue for the first year is $2,000,000. What is the present value of the the toll revenue if the state can earn 6% on their money?

$31,679,745

$37,886,995

$101,601,233

$84,987,673

An engineer estimates that the annual toll revenue from a newly proposed highway construction over 20 years will increase at a rate of 4%. The revenue for the first year is $2,000,000. What is the present value of the the toll revenue if the state can earn 6% on their money?

Explanation / Answer

Present value of toll revenue [P÷(r-g)]×[1-[(1+g)÷(1+r)]^n] Here, 1 Interest rate per annum 6.00% 2 Number of years                                                                                         20 3 Number of compoundings per per annum                                                                                            1 4 = 1÷3 Interest rate per period ( r) 6.00% 5 = 2×3 Number of periods (n) 20 Growth rate (g) 4.00% First payment (P) $                                                                       2,000,000 Present value of toll revenue $                                                                    31,679,745 (2,000,000/(6%-4%))*(1-((1+4%)/(1+6%))^20)

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