a) Both, Present Value and Future Value are related to the process of compounding. Future value refers to the nominal amount to which a current deposit will grow over time when it is placed in an account paying compound interest. In other words, future value is the present value compounded over the years through compounding process. On the other hand, Present Value is the current or value of a given series of payment on a given date. In fact, present value is calculated by discounting the future value through a process called discounting, where an appropriate discounting factor is used to calculate the present value of the given future value of money. The formula given below, will give us a mathematical relationship between present value and future value:
Present Value= Future Value/ (1+ Interest Rate)n
Here, n= Number of compounding periods
b) The calculations involved in the present and future value concepts are basic and are mainly concerned with the discounting/ compounding rate and discounting/ compounding periods. For Instance, If Mr. X would like to have $5000 saved in his account at the end of three years and with 9% return with monthly compounding, the present value of the amount to be deposited will be equal to:
PV= Future Value/ (1+ Interest Rate)n
Important to note that had the amount been compounded yearly, in such case:
c) The concept of Future Value and Present Value are being readily used in our daily life. Apart from the example presented in Part B, the following example of Loan Amortization is another example as how these concepts also relate to real life business situation:
A company plans to borrow $50000 for five years. The company’s bank will lend the money at a rate of 9% and requires that the loan be paid off in one single end-of-the 5 year payment. Calculate the amount of the payments that the company must make in order to fully amortize the loan at the end of five years:
Here, PV= -$50000, N= 5 Years, Interest Rate= 9%, Compounding= Yearly
So, FV= PV(1+ Interest Rate)n
Thus, the company will be required to make one single payment of $76931.20 at the end of five years.
Brown, K. (2011). The Time Value of Money. In C. Institute, Quantitative Methods (pp. 116-119). Boston: Custom.