Note that the account yields 5 interest per year compounded annually From above

# Note that the account yields 5 interest per year

• 17

This preview shows page 13 - 17 out of 17 pages.

Note that the account yields 5% interest per year, compounded annually? From above problem: P = \$10,000 i = 5% n = 5 years Consider uniform series capital recover factor: A = P * (A/P,i%,n) = \$10,000 * (A/P,5%,5) = \$10,000 * 0.23097 = \$2,309.70 Note: 0.23096 is obtained from appendix A compound interest factor for interest rate = 5.00%. Therefore, you need to withdraw \$2,309.70 for 5 years so that the account can be depleted at the end of 5 years. 13 IE 492 Engineering Economics

Subscribe to view the full document.

UNIFORM SERIES PRESENT WORTH FACTOR Uniform series present worth factor calculates the amount that must be invested today in order to be able to withdraw a fixed amount every year for n years, when the invested amount earns interest i per year, compounded annually. Uniform series present worth factor is reciprocal of the uniform series capital recovery factor. Uniform series capital recovery factor formula: A = P * i(1+i) n / [(1 + i) n 1] Therefore, A/P = i(1+i) n / [(1 + i) n 1] = i/[1-(1+i) -n ] Therefore, P/A = (A/P) -1 = [(1 + i) n 1] / i(1+i) n Therefore, the ratio, P/A is called the uniform series present worth factor. Numerical values of this factor are shown in Appendix A of the book. A fuller notation for this factor is: (P/A,i%,n) Let’s look at an example on the next slide. 14 IE 492 Engineering Economics
UNIFORM SERIES PRESENT WORTH FACTOR (EXAMPLE) You decide to withdraw \$2,309.70 at the end of each year from your investment account for 5 years. After 5 years you expect to have depleted the account balance and wish to close the account. How much money should you deposit in the account today, if the account yields 5% interest per year, compounded annually? From above problem: A = \$2,309.70 i = 5% n = 5 years Consider uniform series capital recover factor: P = A * (P/A,i%,n) = A * (A/P,i%,n) -1 = \$2,309.70 * (A/P,5%,5) -1 = \$2,309.70 * (0.23097) -1 = \$10,000 Note: 0.23097 is obtained from appendix A compound interest factor for interest rate = 5.00%. Therefore, you need to withdraw invest \$10,000 today so you can withdraw \$2,309.70 for 5 and account can be depleted after the fifth withdrawal. 15 Note: Uniform series present worth factor is reciprocal of Uniform series capital recovery factor IE 492 Engineering Economics

Subscribe to view the full document.

GRADIENT SERIES FACTOR Gradient series is a series of payments that either increases or decreases each by a constant amount. Payments are made at the end of at the beginning of each period. The delta i.e. increase or decrease amount is called as gradient. If the increase or decrease amount is a constant amount then the series is called as Arithmetic Gradient Uniform Series. E.g. amount is \$500, \$1000, -\$500, -\$2000 etc.
• Summer '16

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern