## Presentation on theme: "Interest Formulas (Gradient Series)"— Presentation transcript:

Lecture No.8 Chapter 3 Contemporary Engineering Economics Copyright © 2006 Contemporary Engineering Economics, 4th edition, © 2007

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 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 \$1,000(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

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