ENGINEERING ECONOMY(LOOSELEAF)
ENGINEERING ECONOMY(LOOSELEAF)
8th Edition
ISBN: 9781260152814
Author: Blank
Publisher: MCG
Question
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Chapter 2, Problem 26P

(1):

To determine

Calculate future value factor to the annual value.

(1):

Expert Solution
Check Mark

Explanation of Solution

Option (a):

Interest rate (i) is 19% and time period (n) is 20.

The future value factor to the annual value (FA) through linear interpolate can be calculated as follows. The interest rate lies between (i1)18% and (i2) 20%.

FA=(1+i1)n1i1((ii1)100(i2i1)100((1+i1)n1i1(1+i2)n1i2))=(1+0.18)2010.18((0.0190.18)100(0.20.18)100((1+0.18)2010.18(1+0.2)2010.2))=27.39310.18((0.01)100(0.02)100(27.39310.1838.337610.2))=146.6278(12(146.6278186.688))=146.6278(12(146.6278186.688))=146.6278(20.301)=166.6579

The future value factor to the annual value is 166.6579.

Option (b):

The future value factor to the annual value (FA) through formula can be calculated as follows:

FA=(1+i)n1i=(1+0.19)2010.19=32.429410.19=165.4179

The future value factor to the annual value is 165.4749.

Option (c):

The future value factor to the annual value (FA) through spreadsheet can be done as follows:

=-FV(i,n,,1)

=-FV(19%,20,,1) This function gives the value of 165.41802.

(2):

To determine

Calculate present value factor to the equivalent annual value.

(2):

Expert Solution
Check Mark

Explanation of Solution

Option (a):

Interest rate (i) is 26% and time period (n) is 15.

The present value factor to the equivalent annual value (PA) through linear interpolate can be calculated as follows. The interest rate is lies between (i1) 25% and (i2) 27%.

PA=(1+i1)n1i1(1+i1)n((ii1)100(i2i1)100((1+i1)n1i1(1+i1)n(1+i2)n1i2(1+i2)n))=(1+0.25)1510.25(1+0.25)15((0.260.25)100(0.270.25)100((1+0.25)1510.25(1+0.25)15(1+0.27)1510.27(1+0.27)15))=28.421710.25(28.4217)((0.01)100(0.02)100(28.421710.25(28.4217)36.062510.27(36.0625)))=27.42177.1054(12(27.42177.105435.06259.7369))=3.8593(0.5(3.85933.601))=3.8593(0.1292)=3.7301

The present value factor to the equivalent annual value is 3.7301.

Option (b):

The present value factor to the equivalent annual value (PA) through formula can be calculated as follows:

PA=(1+i)n1i(1+i)n=(1+0.26)1510.26(1+0.26)15=32.030110.26(32.0301)=31.03018.3278=3.7261

The present value factor to the equivalent annual value is 3.7261.

Option (c):

The present value factor to the equivalent annual value (PA) through spreadsheet can be done as follows:

=-PV(i,n,,1)

=-PV267%,15,,1) This function gives the value of 3.72607.

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ENGINEERING ECONOMY(LOOSELEAF)

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