A student who wants to compute the future value of $500, for example, at the end of 23 years with interest at 5.5 percent compounded annually looks up the factor (the number in the table opposite 23 years in the column headed 5.5 percent), 3.4262, and multiplies that factor by 500. Table 14-1 shows the accumulated amount of 1 at the end of each of 30 years at various rates of compound interest. If the principal is $1, as is shown in most compound interest tables, the formula is S = (1 + i) n. If S represents the future value, or sum, at the end of the period, i the rate of interest, P the principal invested, and n the number of years, the general formula becomes S = P (1 + i) n. The future value of any principal sum invested for any period of time at any rate of interest can be computed by the same process. If this process continues, the accumulated principal and interest will always equal the sum obtained by multiplying $10,000 by 1.055 raised to an exponent equal to the number of years of compound interest earned. If the sum of $11,130 is again invested for another year at 5.5 percent, the principal and interest at the end of the third year will be $11,130 x 1.055, or $11,742, which is the equivalent of multiplying $10,000 by 1.055 3. This is equivalent to multiplying $10,000 by 1.055 2 where the exponent-indicated in this example by the superscript "2"-denotes the number of times the base-in this case 1.055-is multiplied by itself. If the $10,550 is then invested for another year at 5.5 percent, the combined amount of principal and interest at the end of the second year will be $10,550 x 1.055, or $11,130. If you invest $10,000 at 5.5 percent for one year, the combined amount of principal and interest at the end of the year, according to the simple formula previously stated, will be $10,000 x 1.055, or $10,550. This applies compound interest to accumulate interest earnings. The first series shows the amount to which a principal sum of $10,000 invested for a number of years (or other units of time) will increase over time. To understand the relationships, it will be helpful to examine four basic compound interest series. The company’s computations further assume that interest earnings are added to the original principal and reinvested. Premium and reserve computations assume that companies keep funds continuously invested until those funds are paid out in settlement of claims. Life insurance calculations use compound interest.
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