## Simpte lnterest

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,

FVn = 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.