In the preceding Exercises 10 through 15, you computed a number. To do so, first you must decide on the appropriate factor from the tables, and then you use that factor in the appropriate calculation. Notice that you could omit the last step. You could write an arithmetic expression showing the factor you want to use without actually copying down the number and doing the arithmetic. For example, the notation T(i, p, r) means Table I (1, 2, 3, or 4), row p (periods 1 to 20, 22, 24 . . . , 40, 45, 50, 100), and column r (interest rates from 1/2% up to 20%). Thus, T(3, 16, 12) would be the factor in Table 3 for 16 periods and an interest rate of 12% per period, which is 42.75328. Using this notation, you can write an expression for any compound interest problem. A clerk or a computer can evaluate the expression. You can check that you understand this notation by observing that the following are true statements:
T(1, 20, 8) = 4.66096
T(2, 12, 5) = 0.55684
T(3, 16, 12) = 42.75328
T(4, 10, 20) = 4.19247
In the following questions, write an expression for the answer using the notation introduced here, but do not attempt to evaluate the expression.
a. Work the a parts of Exercises 10 through 15.
b. How might your instructor use this notation to write examination questions on compound interest without having to supply you with tables?