INTEREST 73 10. A restaurant keeper sells a meal ticket good for four dollars' worth of meals to be served in a month for $3.75, payable in advance. Assuming that the $4.00 could be paid equitably at the middle of a month of 30 days, what rate of interest is equivalent to the discount ? 11. Construct the graph of the function (1.04)-" with the time as the variable. What is the significance of that part of the graph that lies to the left of the axis of ordinates ? 28. The equation of value. It is frequently necessary to com- pare the value of one set of sums due at various times with another set due at other times. In order that such comparison may be possible, we must observe the following fundamental principle: To compare, several sums due at various times, all the sums must te accumulated or discounted to the same date. In case one set of obligations is equivalent to another set, the relation expressing the fact is called the equation of value. The formation of the equation of value can be best illustrated by an example. Suppose a man owing $1000 due in 18 months, and $500 due in 2 years, wishes to discharge the obligations by two equal payments, one made in 6 months and the other in 1 year. Let the value of each of the two equal payments be denoted by X. We have then to consider four sums: X due in 6 months, X due in 1 year, $1000 due in 18 months, and $500 due in 2 years. If all these sums be discounted to the present, their present values will be Xv^, Xv, 1000 v32, and 500 v2, respectively. By hypothesis, the first two obligations are exactly equivalent to the second two. We have, then, as the equation of value, Xv^ + Xv = 1000 ^ + 500 v\ (1) This equation, evidently, suffices to determine the value of the unknown number X. The time to which all the sums are accumulated, or discounted, is wholly immaterial. For example, if, in the present problem, we accumulate the various sums to the last date, the accumula- tion periods will be 1^, 1, ^, and 0 years, respectively. The equa- tion of value will then be x(\ + iy + ^(i + o = 1000 (i + o^ + 500 (i + 0°.