tailieunhanh - Design and Optimization of Thermal Systems Episode 2 Part 8

Tham khảo tài liệu 'design and optimization of thermal systems episode 2 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Economic Considerations 397 PW FW I I I I I I I Jl Jl I 5 I I I ------------------------------------------------------------------------------------------ 1 II 2 3 4 n I I I I I I I I I I I Present Future FIGURE A uniform series of annual payments and locations of the present and future time frames shown on the time coordinate axis in terms of number of years n. Therefore summing this geometric series which has n terms and a factor of 1 i we have F S qt-O-i S 1 i 1 S F S i n where F S is often known as the series future worth factor or the series compound amount factor. It yields the future worth of a series of payments of equal amount S when S is multiplied by this factor. The amount S of a series of payments to pay off an amount F due at a future date may also be calculated from Equation . Different payment frequencies may similarly be considered. If m payments are made yearly with compounding also done at this frequency the future worth is given by the expression F S I F S f mn S m 1 i m mn -1 i m Therefore the cumulative value of a series of payments on a future date or the amount of each payment for a given future worth may be calculated for different compounding frequencies. Other cases where the payment and compounding schedules are different are also possible and are discussed later. Present Worth of Uniform Series of Amounts The present worth of a series of equal amounts paid at the end of the year for a number of years n starting at the end of the first year as shown in Figure is also obtained easily from the corresponding expression for the future worth by using the present worth factor P F. Therefore for payments made at the end of each year and with annual compounding the present worth P is given by P F P F i n S 1 i n - 1 i P F i n S 1 i n - 1 I 1 i J 1 i n 398 Design and Optimization of Thermal Systems Therefore 1 i n -1 i 1 i n S P S i n P S where P S is the series present worth factor. Similarly if m payments are .