PrintInteresting Discounts
In the example in the text, 1000 dollars this year becomes 1040 dollars next year after the bank adds the interest. You can say that the present value is P, the future value F, the interest i=F-P, and the interest rate r=i/P=(F-P)/P. The discount rate is d=(F-P)/F. A little algebra will show you that d=r/(1+r) and r=d/(1-d). Here r and d are in the decimal forms (0.04, not 4%). In the main text, we will use D=100d for the discount rate in percent. The economic models eventually assume a discount rate, such as 4%, but often you will see calculations made with 3% and 5%, and sometimes 1% and 7%, because the discount rate is quite uncertain. This uncertainty in the discount rate is much larger than the difference between the interest and discount rates, so using either one will get you close.
The example in the text used an interest rate of 0.04, which gives d=0.04/(1+0.04)=0.03846. . . , which looks messy. But, we could have taken d=0.04, which would have given r=0.04/(1-0.04)=0.041666. . ., which makes the interest rate look messy. Your bank may indeed advertise interest rates such as '4.17%!!!'
Inflation is the tendency for all prices and wages to rise in an economy. Measuring inflation is not a trivial task, but useful estimates are available for the inflation rate at different times in different places. Mathematically, it is not difficult to remove the effects of inflation - if everything goes up together, we can correct everything together, reducing the values back to what they would have been at some chosen time (or inflating them to what they will be at some other chosen time). When effects of inflation have been removed from a calculation, you may see costs and benefits referred to in 'constant dollars' or '2005 dollars' or '(some other specific year) dollars' in a government report on decision-making about energy.