Engineering Economy
Engineering Economy
8th Edition
ISBN: 9780073523439
Author: Leland T Blank Professor Emeritus, Anthony Tarquin
Publisher: McGraw-Hill Education
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Chapter 2, Problem 27P

(1):

To determine

Calculate value factor to the present value.

(1):

Expert Solution
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Explanation of Solution

Option (a):

Interest rate (i) is 18% and time period (n) is 33.

The future value factor to the present value (FP) through linear interpolate can be calculated as follows. The interest rate lies between (i1)17% and (i2) 19%.

FP=(1+i1)n((ii1)100(i2i1)100((1+i1)n(1+i2)n))=(1+0.17)33((0.180.17)100(0.190.17)100((1+0.17)33(1+0.19)33))=177.8826((0.01)100(0.02)100(177.8826311.2073))=177.8826(12(177.8826311.2073))=177.8826(66.6624)=244.545

The future value factor to the present value is 244.545.

Option (b):

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

FP=(1+i)n=(1+0.18)33=235.5625

The future value factor to the present value is 235.5625.

(2):

To determine

Calculate annual growth rate.

(2):

Expert Solution
Check Mark

Explanation of Solution

Option (a):

Interest rate (i) is 12% and time period (n) is 54.

The annual growth rate value (AG) through linear interpolate can be calculated as follows. The interest rate lies between (i1) 11% and (i2) 13%.

AG=(1i1n(1+i1)n1)((ii1)100(i2i1)100((1i1n(1+i1)n1)(1i2n(1+i2)n1)))=(10.1154(1+0.11)541)((0.120.11)100(0.130.11)100((10.1154(1+0.11)541)(10.1354(1+0.13)541)))=(9.090954280.18241)((0.01)100(0.02)100((9.090954280.18241)(7.692354734.9131)))=(9.09090.1934)(12((9.09090.1934)(7.69230.0736)))=8.8975(0.5(8.89757.6187))=8.89750.6394=8.3356

The annual growth factor value is 8.3356.

Option (b):

The annual growth factor value (AG) through formula can be calculated as follows:

PA=(1in(1+i)n1)=(10.1254(1+0.12)541)=(8.333354454.75051)=(8.33330.119)=8.2143

The annual growth factor value is 8.2143.

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Engineering Economy

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