contemporary engineering economics, 6 th edition park copyright © 2016 by pearson education, inc....

Contemporary Engineering Economics, 6th editionPark

Copyright © 2016 by Pearson Education, Inc.All Rights Reserved

Interest Formulas for Single Cash Flows

Lecture No. 6Chapter 3

Contemporary Engineering EconomicsCopyright © 2016

Contemporary Engineering Economics, 6th editionPark

Copyright © 2016 by Pearson Education, Inc.All Rights Reserved

Types of Common Cash Flows in Engineering Economics

Single cash flow Equal (uniform) payment series at regular intervals Linear gradient series Geometric gradient series Irregular (random) payment series

Contemporary Engineering Economics, 6th editionPark

Copyright © 2016 by Pearson Education, Inc.All Rights Reserved

Equivalence Relationship Between P and F

Compounding ProcessFinding an equivalent future value of a current cash payment

Discounting Process Finding an equivalent present value of a future cash payment

Contemporary Engineering Economics, 6th editionPark

Copyright © 2016 by Pearson Education, Inc.All Rights Reserved

Singe Cash Flow FormulaCompound Amount Factor

Contemporary Engineering Economics, 6th editionPark

Copyright © 2016 by Pearson Education, Inc.All Rights Reserved

Example 3.7: Find F, Given i, N, and P

Excel SolutionGiven: P = $2,000, i = 10%, N = 8 years

Find: F

8$2,000(1 0.10)$2,000( / ,10%,8)$4,287.18

FF P

Contemporary Engineering Economics, 6th editionPark

Copyright © 2016 by Pearson Education, Inc.All Rights Reserved

A Typical Compound Interest Table at 12%

To find the compound interest factor when the interest rate is 12% and the number of interest periods is 10, we could evaluate the following equation using the interest table.

Contemporary Engineering Economics, 6th editionPark

Copyright © 2016 by Pearson Education, Inc.All Rights Reserved

Single Cash Flow FormulaPresent Worth Amount Factor

Contemporary Engineering Economics, 6th editionPark

Copyright © 2016 by Pearson Education, Inc.All Rights Reserved

Example 3.8: Find P, Given i, N, and F

Given: F = $1,000, i = 12%, N = 5 years

Find: P

Excel Solution

5$1,000(1 0.12)$1,000( / ,12%,5)$567.43

PP F

Contemporary Engineering Economics, 6th editionPark

Copyright © 2016 by Pearson Education, Inc.All Rights Reserved

Example 3.9: Find i, Given P, F, and N

• Cash Flow DiagramGiven: F = $20, P = $10, N = 5 yearsFind: i

Excel Solution

Contemporary Engineering Economics, 6th editionPark

Copyright © 2016 by Pearson Education, Inc.All Rights Reserved

Example 3.10: Find N, Given P, F, and i

• Solving for N Given: P = $6,000, F = $12,000, i = 20%Find: N

Excel Solution

2 (1 0.20)

2 1.2 log2 log1.2

log2log1.23.80 years

N

N

F P P

N

N

Contemporary Engineering Economics, 6th editionPark

Copyright © 2016 by Pearson Education, Inc.All Rights Reserved

Rule of 72• Number of Years Required to Double an

Initial Investment at Various Interest RatesApproximating how long it will take for a sum of money to double

72interest rate (%)72203.6 years

N