ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
Question
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Chapter 3, Problem 53P
To determine

(a)

The effective interest rate.

Expert Solution
Check Mark

Answer to Problem 53P

The Effective Interest rate in this case is 4.06%.

Explanation of Solution

Given information:

  • The nominal annual interest rate = 4%
  • Compounded every three months
  • Effective Interest Rate per year is the annual interest rate taking into account the effect of any compounding during the year. It is calculated as
  • ia=(1+rm)m1

    where: ia = effective interest rate

    r = nominal interest rate

    m = number of compounding subperiods per year

  • Nominal Interest Rate per year is the annual interest rate without taking into account the effect of any compounding during the year. It is calculated as:

    r=(m×im)

    where: r = nominal interest rate

    m = number of compounding subperiods per year

    im = interest rate during the compounding subperiod

Calculation:

Using the information given in the question, one knows m = 4 since the interest rate is compounding the subperiods on a quarterly basis. We need to find the effective annual interest rate to using the value of the nominal annual interest rate given in the question:

ia=(1+rm)m1ia=(1+r400)41ia=(1+4400)121ia=(1+0.01)41ia=(1.01)41ia=1.04061ia=0.0406ia=4.06%

Therefore, effective annual interest rate is 4.06%.

To determine

(b)

The effective interest rate.

Expert Solution
Check Mark

Answer to Problem 53P

The effective Interest rate in this case is 4.040584%.

Explanation of Solution

Given information:

  • The nominal annual interest rate = 4%
  • Compounded every daily
  • Effective Interest Rate per year is the annual interest rate taking into account the effect of any compounding during the year. It is calculated as
  • ia=(1+rm)m1

    where: ia = effective interest rate

    r = nominal interest rate

    m = number of compounding subperiods per year

  • Nominal Interest Rate per year is the annual interest rate without taking into account the effect of any compounding during the year. It is calculated as:

    r=(m×im)

    where: r = nominal interest rate

    m = number of compounding subperiods per year

    im = interest rate during the compounding subperiod

Calculation:

Using the information given in the question, one knows m = 4 since the interest rate is compounding the subperiods on a daily basis. We need to find the effective annual interest rate to using the value of the nominal annual interest rate given in the question:

ia=(1+rm)m1ia=(1+r36500)3651ia=(1+436500)3651ia=(1+0.000109)3651ia=(1.000109)3651ia=1.0405841ia=0.040584ia=4.0584%

Therefore, effective annual interest rate is 4.040584%.

To determine

(c)

The effective interest rate.

Expert Solution
Check Mark

Answer to Problem 53P

Effective Interest rate in this case is 4.08%.

Explanation of Solution

Given information:

  • The nominal interest per month = 4%
  • Compounded continuously
  • Effective Interest Rate per year is the annual interest rate taking into account the effect of any compounding during the year. It is calculated as

    ia=(1+rm)m1

    where: ia = effective interest rate

    r = nominal interest rate

    m = number of compounding subperiods per year

    When the interest rate is compounded continuously:

    ia=er1

Calculation:

After inserting the value of nominal interest rate as calculated above in the effective interest rate formula:

ia=er1ia=e0.041ia=1.04081ia=0.0408ia=4.08%

Therefore, effective interest rate is 4.08%.

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