## Info

2.231%

In = the amount of accumulated interest over n years; and n = the number of years between P and F.

The goal of studying the mathematics of interest is to develop a formula for Fn which is expressed only in terms of the present amount P, the annual interest rate i, and the number of years n. There are two major approaches for determining the value of In; simple interest and compound interest. Under simple interest, interest is earned (charged) only on the original amount loaned (borrowed). Under compound interest, interest is earned (charged) on the original amount loaned (borrowed) plus any interest accumulated from previous periods.

4.6.3 Simple Interest

For simple interest, interest is earned (charged) only on the original principal amount at the rate of i%

per year (expressed as i%/yr). Table 4.4 illustrates the annual calculation of simple interest. In Table 4.4 and the formulas which follow, the interest rate i is to be expressed as a decimal amount (e.g., 8% interest is expressed as 0.08).

At the beginning of year 1 (end of year 0), P dollars (e.g., \$100) are deposited in an account earning i%/yr (e.g., 8%/yr or 0.08) simple interest. Under simple compounding, during year 1 the P dollars (\$100) earn P*i dollars (\$100*0.08 = \$8) of interest. At the end of the year 1 the balance in the account is obtained by adding P dollars (the original principal, \$100) plus P*i (the interest earned during year 1, \$8) to obtain P+P*i (\$100+\$8=\$108). Through algebraic manipulation, the end of year 1 balance can be expressed mathematically as P*(1+i) dollars (\$100*1.08=\$108).

The beginning of year 2 is the same point in time as the end of year 1 so the balance in the account is P*(1+i) dollars (\$108). During year 2 the account again

Table 4.4 The mathematics of simple interest

Year (t)

Amount At Beginning Of Year

Interest Earned During Year

Amount At End Of Year (Ft)

0 0