Suppose I have computed the cost of carbon per mile for my car at 0.009 per mile. Assume that the interest rate is 5% and that I drive the car 20,000 miles per year. What is present value of the carbon expense for five years? You will need to use the PV function in Excel or a financial calculator. In Excel the present value of a stream of monetary cash flows is given by PV(rate,number of payments,payment amount) where rate is the interest rate.
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Can we assume that the car is driven continuously throughout the year? – user130512 Mar 13 '14 at 13:55
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Thanks for the Excel hints… but how does the environment charge interest on carbon emissions? Or is "carbon" just the new slang for gasoline and you're paying at the pump with credit? – Potatoswatter Apr 22 '14 at 04:39
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Based on the assumptions in my comment (which is most realistic), the present value of the annuity can be represented by:
$$PV=PMT\frac{1-(1+i)^{-n}}{\delta}$$where $PMT=(0.009)(20000)$, $i=0.05$, $n=5$ and $\delta=ln(1+i)$
Solving, the present value becomes: $798.63$
If the payments are made at the end of each year for the cost of the car, then the formula becomes:$$PV=PMT\frac{1-(1+i)^{-n}}{i}$$
user130512
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