Investment Science: Present Value and Future Value of an investment

Monday, August 16, 2010

This article answers the questions

1. What is the present value and future value of an investment?
2. What is the relationship between the present value and future value of an investment?

1. What is the present value and future value of an investment?

Lets take an example, assume that you invest $1000 in a bank for 2 years at an interest rate 10% (compounded yearly), after 2 years, the growth of the investment is

Growth = 1000 * (1 + 10/100) ^ 2 = 1210
 
The growth of an investment (under compound interest) is known as the "Future value" of an investment.
The amount invested initially to attain that growth is called the "Present value" of an investment.
 
Suppose that you have a current bank balance of $1210 that pays 10% interest, what's the investment's worth two years back, clearly it's worth 1210 / (1 + 10/100) ^ 2 = $1000

Now we have a relationship between present value and the future value of an investment.

2. What is the relationship between the present value and future value of an investment?

For an investment compounded at an yearly interest rate 'r' for 'n' years at a present value PV, the future value FV is given by, 


 where (1 + r) ^ n is called as the growth factor.



where 1 / (1 + r) ^ n is called the discount factor.

If the investment is compounded at 'm' periods per year at an interest rate 'r', then after 'n' years,



and


An investor would always make a decision based on the present value analysis (or maximizing the Net Present Value), for a simple investment like the one shown above, it's easy to calculate the present value, but for an investment which involves a cash flow stream which is not uniform, it's not as trivial as shown above, which brings us to our next article, which will be on understanding more on cash flow streams.

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