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

Note that the account yields 5 interest per year

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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
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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
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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
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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.
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