Interest Formulas (Gradient Series) Lecture No.8 Chapter 3 Contemporary Engineering Economics Copyright © 2006 Contemporary Engineering Economics, 4th edition, © 2007

Linear Gradient Series P Contemporary Engineering Economics, 4th edition, © 2007

Contemporary Engineering Economics, 4th edition, © 2007 Gradient Series as a Composite Series of a Uniform Series of N Payments of A1 and the Gradient Series of Increments of Constant Amount G. Contemporary Engineering Economics, 4th edition, © 2007

Example – Present value calculation for a gradient series $2,000 $1,750 $1,500 $1,250 $1,000 1 2 3 4 5 How much do you have to deposit now in a savings account that earns a 12% annual interest, if you want to withdraw the annual series as shown in the figure? P =? Contemporary Engineering Economics, 4th edition, © 2007

Contemporary Engineering Economics, 4th edition, © 2007 Method 1: Using the (P/F, i, N) Factor $2,000 $1,750 $1,500 $1,250 $1,000 1 2 3 4 5 $1,000(P/F, 12%, 1) = $892.86 $1,250(P/F, 12%, 2) = $996.49 $1,500(P/F, 12%, 3) = $1,067.67 $1,750(P/F, 12%, 4) = $1,112.16 $2,000(P/F, 12%, 5) = $1,134.85 $5,204.03 P =? Contemporary Engineering Economics, 4th edition, © 2007

Method 2: Using the Gradient Factor Contemporary Engineering Economics, 4th edition, © 2007

Gradient-to-Equal-Payment Series Conversion Factor, (A/G, i, N) Contemporary Engineering Economics, 4th edition, © 2007

Example 3.21 – Find the Equivalent Uniform Deposit Plan Contemporary Engineering Economics, 4th edition, © 2007

Contemporary Engineering Economics, 4th edition, © 2007 Solution: Contemporary Engineering Economics, 4th edition, © 2007

Example 3.22 Declining Linear Gradient Series Contemporary Engineering Economics, 4th edition, © 2007

Contemporary Engineering Economics, 4th edition, © 2007 Solution: Contemporary Engineering Economics, 4th edition, © 2007

Types of Geometric Gradient Series Contemporary Engineering Economics, 4th edition, © 2007

Contemporary Engineering Economics, 4th edition, © 2007 Present Worth Factor Contemporary Engineering Economics, 4th edition, © 2007

Example 3.23 Annual Power Cost if Repair is Not Performed Contemporary Engineering Economics, 4th edition, © 2007

Solution – Adopt the new compressed-air system Contemporary Engineering Economics, 4th edition, © 2007

Example 3.24 Jimmy Carpenter’s Retirement Plan – Save $1 Million Contemporary Engineering Economics, 4th edition, © 2007

What Should be the Size of his first Deposit (A1)? Contemporary Engineering Economics, 4th edition, © 2007