Engineering Economic Analysis
Engineering Economic Analysis
13th Edition
ISBN: 9780190296902
Author: Donald G. Newnan, Ted G. Eschenbach, Jerome P. Lavelle
Publisher: Oxford University Press
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Chapter 3, Problem 5P
To determine

The interest and total amount due at the end of the loan for both simple and compound interest.

Expert Solution & Answer
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Answer to Problem 5P

The interest and total amount due at the end of the loan for both simple and compound interest is shown in the table below.

SI As CI Ac
(a) $100 $1100 $1102.50 $102.5
(b) $450 $1950 $2007.34 $507.34
(c) $10000 $20000 $25937.42 $15937.42
(d) $562500 $81250 $203426.54 $178426.54
(e) $191000 $238750 $1830620.40 $1782870.40

Explanation of Solution

Given:

Loan Years Rate
(a) $1000 2 5%
(b) $1500 5 6%
(c) $10,000 10 10%
(d) $25,000 15 15%
(e) $47,750 20 20%

Concept used:

Write the expression to calculate simple interest.

SI=P×R×T100 ...... (I)

Here, simple interest is SI, principal amount is

P, interest rate is

R and time period is T.

Write the expression to calculate the amount due to simple interest.

As=P+SI ...... (II)

Here, amount due to simple interest is As.

Write the expression to calculate compound interest.

CI=P(1+R100)T ...... (III)

Here, compound interest is CI.

Write the expression to calculate the amount due to compound interest.

Ac=CIP ...... (IV)

Here, the amount due to compound interest is Ac. R.

Calculation:

Calculate the simple interest.

Substitute $1000 for P, 5 for and 2 for T in Equation (I).

SI=$1000×5×2100=$100

Calculate the amount due to simple interest.

Substitute $100 for SI and $1000 for P in Equation (II).

As=$1000+$100=$1100

Calculate the compound interest.

Substitute $1000 for P, 5% for R and 2 for T in Equation (III).

CI=$1000(1+5100)2=$1102.50

Calculate the amount due to compound interest.

Substitute $1102.5 for CI and $1000 for P in Equation (IV).

Ac=$1102.50$1000=$102.5

The values for the loan values are calculated and shown below in the table.

Loan Years Rate SI As CI Ac
(a) $1000 2 5% $100 $1100 $1102.50 $102.5
(b) $1500 5 6% $450 $1950 $2007.34 $507.34
(c) $10,000 10 10% $10000 $20000 $25937.42 $15937.42
(d) $25,000 15 15% $562500 $81250 $203426.54 $178426.54
(e) $47,750 20 20% $191000 $238750 $1830620.40 $1782870.40

Here, SI is calculated from Equation (I), As is calculated from Equation (II), CI is calculated from Equation (III) and Ac is calculated from Equation (IV).

Conclusion:

Thus, the interest and total amount is shown in the following table.

SI As CI Ac
(a) $100 $1100 $1102.50 $102.5
(b) $450 $1950 $2007.34 $507.34
(c) $10000 $20000 $25937.42 $15937.42
(d) $562500 $81250 $203426.54 $178426.54
(e) $191000 $238750 $1830620.40 $1782870.40

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