Whattya Know Break

1. Compound interest is just the reverse of present discounted value.

To find the future value of a sum of money invested in a savings account or another income-earning asset at a stated rate of interest we use the formula future value = present value * (1+r)ⁿ. n is the number of years.

Example: We invest $100 in a savings account that earns 5% interest annually. $100 is the present value. If we leave it in the bank for two years it will have a future value of:

     Future Value = $100 * (1.05)²

    Future Value = $100 * 1.1025

Future Value = $110.25

If the current rate of interest is 5% and someone asked what we would pay for a promise of $110.25 to be given to us in two years we would say, "no more than $100." Why? Because we know that we can place $100 in a bank at 5% interest and get exactly $110.25 in two years.

We just rearrange the future value formula to get the present discounted value formula (PDV is the same as present value):

                                                       PDV = Future value/ (1+r)ⁿ.

                                                       PDV = $110.25/ (1+r)ⁿ

                                                       PDV = $110.25/1.1025 = $100

Application to Environmental Economics: Neoclassical economists who are concerned about the environment but still want to measure the costs and benefits of taking protective action will discount the value of a harm that won't befall us until some time in the future. Using the example above, neoclassical economists would argue that we should pay only $100 or less today to protect us from an environmental disaster that will occur two years from now, costing us $110.25 at that time. Why? Because we could invest $100 today at the going interest rate of 5% and have $110.25 in two years to take care of the environmental disaster then. This is not a false choice from neoclassical economists' perspectives. Moreover, it is the way government makes decisions.

The difficult question is what discount rate should be used. The answer neoclassical economists offer is the rate of growth of NNW. Why? Because (assuming NNW growth rate = 5% annually) if protection costs us more than $100 today we could do nothing now (allowing the $100 to be invested in economic activity) and the annual rate of growth of NNW would produce enough added value to cover the cost of the $110.25 disaster when it arrives.  But if NNW grows at close to zero, which is more likely, it would be better to take care of the problem now. A $110.25 disaster occurring two years from now is worth $110.25 to us today at a zero discount rate. No government agency uses a discount rate lower than 3% meaning they don't take future environmental disasters as seriously as they should.