Engineering Economy
Engineering Economy
8th Edition
ISBN: 9780073523439
Author: Leland T Blank Professor Emeritus, Anthony Tarquin
Publisher: McGraw-Hill Education
Question
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Chapter 4, Problem 44P

(a):

To determine

Calculate the equivalent monthly value.

(a):

Expert Solution
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Explanation of Solution

The borrowing (B) is $80,000. The interest rate (i1) is 6% per year and it is compounded semiannually for two payments. The effective interest rate 1 (Ei1) is 0.5% (612). The interest rate (i2) is 4.2% per year and it is compounded semiannually for third payments. The effective interest rate 2 (Ei2) is 0.35% (4.212). The time period (n) is 60 months (12×5).

The equivalent monthly value (A) can be calculated as follows:

A=B(Ei1(1+Ei1)n(1+Ei1)n1)=80,000(0.005(1+0.005)60(1+0.005)601)=80,000(0.005(1.3488502)1.34885021)=80,000(0.00674430.3488502)=80,000(0.01933)=1,546.4

The equivalent monthly value is $1,546.4.

(b):

To determine

Calculate the current balance.

(b):

Expert Solution
Check Mark

Explanation of Solution

The interest payment in the first year can be calculated as follows:

Interest payment 1=B×Ei1=80,000×0.005=400

The interest payment for the first year is $400.

The interest payment in the second year can be calculated as follows:

Interest payment 2=(B(AInterest payment 1))×Ei=(80,000(1,546.40400))×0.005=(80,0001,146.40)×0.005=78,853360×0.005=394.27

The interest payment for the second year is $394.27.

The current principal payment (CP) can be calculated as follows:

CP=B((A×2)(Interest payment 1Interest payment 2))=80,000((1,546.4×2)400394.27)=80,000(3,092.8400394.27)=80,0002,298.53=77,701.47

The current principal payment is $77,701.47.

(c):

To determine

Calculate the total interest payment.

(c):

Expert Solution
Check Mark

Explanation of Solution

The total interest payment for the first two years can be calculated as follows:

Total interest payment=(Interest payment 1+Interest payment 2)=400+394.27=794.27

The total interest payment for the first two years is $794.27.

(d):

To determine

Calculate the equivalent monthly value.

(d):

Expert Solution
Check Mark

Explanation of Solution

The borrowing (B) is $80,000. The interest rate (i1) is 6% per year and it is compounded semiannually for two payments. The effective interest rate 1 (Ei1) is 0.5% (612). The interest rate (i2) is 4.2% per year and it is compounded semiannually for third payment. The effective interest rate 2 (Ei2) is 0.35% (4.212). The time period (n) is 60 months (12×5).

The equivalent monthly value (A) for second loan can be calculated as follows:

A=Current principal payment(Ei2(1+Ei2)n(1+Ei2)n1)=77,701.47(0.0035(1+0.0035)60(1+0.0035)601)=77,701.47(0.0035(1.233226)1.2332261)=77,701.47(0.0043160.233226)=77,701.47(0.018506)=1,437.94

The equivalent monthly value is $1,437.94.

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Chapter 4 Solutions

Engineering Economy

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