Simple interest is interest that is paid (earned) on only the original amount, or principal, borrowed (lent). The dollar amount of simple interest is a funciion of three variables: the originai amount borrowed (lent), or principal; the interest rate per time period; and the number of time periods for which the principal is borrowed (lentj. The foimula for calculating simple interest is

SI = P₀(i)(n)

where SI = simple interest in dollars

P₀ = principal, or original amount borrowed (lent) at time period 0

i = interest rate per time period

n = number of time periods

For example, assume that you deposit $100 in a savings account paylng 8 percent simple interest and keep it there for 10 years. At the end of 10 years, the amount of interest accumulated is determined as follows:

$80 = $100(0.08)(10)

To solve for the future value (also knovm as the terminal value) of the account at the end of 10 years (FV₁₀), we add the interest earned on the principal only to the original amount invested. Therefore

FV₀ = $100 + [$100(0.08)(10)]= $180

For any simple interest rate, the future value of an account at the end. of n periods is or, equivalently,

FV_n = P₀ + SI = P₀ + P₀(i)(n)

or, equivalently,

FVn = P₀[1+ (i)(n)]                        (3.2)

Sometimes we need to proceed in the opposite direction. That is, we know the future value of a deposit at I percent for zl years, but we don't know the principal originally invested - the account's present value (PV₀=P₀). A rearrangement of Eq. (3.2), however, is all that is needed.

PV₀ = P₀ = FV₀⁄[1+ (i)(n)]            (3.3)

Now that you are familiar with the mechanics of simple interest, it is perhaps a bit cruel to point out that most situations in finance involving the time value of money do not rely on simple interest at all. Instead, compound interest is the norm; however, an understanding of simple interest will help you appreciate (and understand) compound interest all the more.