The Investment Formula
The Investment Formula
The investment formula is used when an investor wants to invest a single amount, called the principal amount, into an account at a fixed interest rate for a certain amount of time. Like with all things, we will remember and understand this formula better if we derived it in a logical way so that the formula makes sense to us.
(For the purposes of this write-up we are going to look at compound interest, which is compounded only yearly)
• If we invest an amount of money, the principal P, into a bank account at an interest rate of i for 1 year, our money will be worth [pic] at the end of that year. To understand this formula apply the distributive law and you will see that you will get your money back at the end of the year [pic] and you will get interest on your money, which is [pic].
• Now if you plan to invest your money for a second year, your new principal is [pic] because that is how much money you now have. This amount will draw interest for 1 year, again at an interest rate of i. At the end of that year, you will have [pic].
• If you repeat this process for n years, your single investment of P will be worth [pic].
Therefore the investment formula for a principal P, an interest rate i and a term n is [pic].
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