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.
2026-03-27 00:06:47.1774570007
What is present value of the carbon expense for five years?
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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:$$PV=PMT\frac{1-(1+i)^{-n}}{i}$$