In macroeconomics, two important financial structures are the present value and future value. Below is a discussion describing the two structures, and how they differ from one another.
Present versus future value is analogous to the concept that today's dollar will be worth more in the future. This concept is realized when that dollar is invested or put into savings. Assuming no risk, in the future, that dollar will have accumulated interest. Compounding interest is when the interest and the original principle are reinvested to accumulate interest on the larger whole.
One can then determine the future value of money by using financial tables and formula along with the present value. Defining the present value (PV) as the cash in hand today that will be invested, and the future value (FV) as the amount of money you will possess when the investment has matured, you can then take the interest (I) per compounding period and the number (n) of periods between the present and future and compute FV = PV*(1+I)^n. That is, multiply the present value by one plus the interest n times in order to get the future value.
As an example, lets say you have a 5% APR savings account, which is compounded daily and you invest $100 dollars in. The interest per day is .05/365 = .0137%. At the end of one year, the future value of the savings account is $100*(1+.000137)^365 = $105.13.
Suppose you wish to know how much to invest in order to obtain a particular future value. This can be computed from the above formula, by dividing the compounded interest and obtaining PV = FV/(1+I)^n. Lets take the interest above, and suppose we want to have $1500 at the end of five years. Using our formula, $1500/(1+.000137)^(365*5) = $1168.23.
These examples can be applied to any sort of investment or debt where interest is accumulated or charged. When you factor in monthly payments, you have to make a computation at every month. For example, suppose you start as in the first example, investing $100 at 5% APR compounded daily. Now suppose you deposit $100 per month. The procedure is to compute the future value after a month, and add $100 to it. It then becomes the new "present value," and the cycle repeats. So, with figures, FV = $100*(1+.000137)^30 = $100.41. Add the deposit, and the new PV is $200.41. The next month, FV = $200.41*(1+.000137)^30 = $201.24. The process continues on and on.
This method also works to figure out how much you will really pay with a credit card debt. Suppose you charge $1000 to a card with 10% APR, compounded daily. You make a $100 payment every month. How long until you have paid off your card, and how much did you pay in total? Well, after one month, FV = $1000*(1+.10/365)^30 = $1008.25. You make your payment, which leaves $908.25. The next month, FV = $908.25*(1+.10/365)^30 = $916.75. Repeating the process will lead to your paying off the debt in 11 months, and paying a total amount of $1048.08. In other words, the $1000 you borrowed today, the present value, will hold a future value of around $1050 for the credit card company. After a year, you have lost $50 dollars in order to have the $1000 up front. Imagine if you only made minimum payments, which are around $20~ish dollars. You would end up paying a lot more in the long run.
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Originally posted 2009-03-19 05:40:44. Republished by Blog Post Promoter
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In a deflation, it is also important to know the future value of the cash or assets you are holding.
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