Financial Literacy

Unit 2 – Time Value of Money

Lesson 2.5: Present Value & Future Value

We will be focusing our attention on two of the five components that make up the Time Value of Money calculation: Present Value and Future Value.  We will discuss their definitions, how to calculate for these variables, and provide you with some examples of how they factor into financial planning.

1. Present Value

   Present Value (PV) details the current value associated with a sum of money that is to be received in the future, in today’s dollars.  This future sum of money can be in the form of a lump-sum amount at a future date, or a stream of income that will run in the future.  Essentially, what Present Value determines is how much a future amount of money is worth today.  When considering Financial Planning, it can be used to determine the amount they will need to save today, in order to satisfy a specific goal in the future.

    

   The mathematical formula to determine Present Value (PV) is as follows:
              

   Present Value (PV) =FV
                                     (1+i)ⁿ

   FV = Future Value
   i = Interest Rate
   n = Number of Periods Expressed in Years

    

   Example – Present Value
   In this example, you are determining if you have enough money to purchase a car in 5 years’ time. You know that in exactly 5 years you will need $30,000, and you can hold your money in an account that guarantees an annual Real Interest Rate of 6%.  Your concern is how much money you will have to set aside today to ensure that you will have the $30,000 in 5 years.

   Present Value (PV) = FV
                                     (1+i)ⁿ
   Present Value (PV) = $30,000
                                     (1+0.06)⁵

   $30,000 = FV = Future Value
   6% 0r 0.06 = i = Interest Rate
   5 = n = Number of Periods Expressed in Years

   Using the Present Value formula, we can determine what the Present Value is for an investment earning 6% per year, for five years, to determine how much you will be required to invest today. 

   Based on this calculation, you determine that the Present Value for this situation is $22,417.75.  What this means is given you invest your assets for 5 years at 6% Rate-of-Return (Interest Rate) per year, you will need to save $22,417.75 today to be able to purchase the car.

    

2. Future Value

   On the contrary, Future Value (FV) refers to the final amount (known as the terminal amount) one can expect for an investment if the investment compounds at a given Rate-of-Return (Interest Rate) for a given period of time. 

   The mathematical formula to determine Future Value (FV) is as follows:

    

   Future Value (FV) = PV x (1+i)ⁿ

   PV = Present Value
   i = Interest Rate
   n = Number of Periods Expressed in Years

   Example – Future Value

   In this example, you are determining if you really need that new car after all, and whether you would be better served saving for your retirement instead.  You decide to use the Future Value formula to determine what the $22,417.75 could look like when you retire in 30 years.  Assuming that you would be utilizing the same investment, offering 6% Rate-of-Return, per year, what would the Future Value of your retirement assets be if you didn’t end up buying the new car?

   Future Value (FV) = PV x (1+i)ⁿ
   Future Value (FV) = $22,417.75 x (1+0.06)³⁰

   $22,417.75 = PV = Present Value
   6% or 0.06 = i = Interest Rate
   5 = n = Number of Periods Expressed in Years

   After performing the calculations, you determine that if you invest the $22,417.75 today, you will have $128,756.15 when you retire.  Maybe you don’t decide to get that car after all.

 

Streams of Payments

In both of our examples, we have discussed the ways in which you can calculate Present Value and Future Value based on lump-sum savings amounts or lump-sum amounts needed.  These calculations can also be made to determine the Present Value and Future Value of continuous streams of payments, although this makes the formula much more complicated. 

 

Summary

Present Value and Future Value calculations allow for individuals to compare different financial strategies to determine either how much money they need to save now or how much money they will need saved in the future to meet their financial objectives.  Obviously, for certain simple calculations, such as the two examples provided in this Lesson, they can be done by hand, but as the situations become more and more complex, individuals establishing financial planning strategies will need to rely on financial calculators and projection programs.  Even so, the principles remain the same, and Present Value and Future Value calculations are integral components to financial planning.

In Lesson 2.6 we will discuss how individuals can put the Time Value of Money Calculations into practice with real life examples that can aid any individual in their financial planning.