   Chapter 4.6, Problem 36E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Effective Rate Use the results of Exercise 35 to complete the table showing the effective rates for nominal rates of (a) r =   5 % , (b) r =   6 % , and (c) r   = 7 1 2 % . Number of compoundings per year 4 12 365 Continuous Effective rate

(a)

To determine

To calculate: The effective rate of interest reff for the nominal rate of interest r=5% compounded 4, 12, 365 times and continuously and fill the following table:

 Number of compounding per year 4 12 365 Continuously Effective rate
Explanation

Given Information:

The provided nominal rate of interest r=5% and the provided table to be filled is:

 Number of compounding per year 4 12 365 Continuously Effective rate

Formula used:

The effective rate of interest reff that will produce the same interest per year as the nominal rate r compounded n times per year is given by the formula:

reff=(1+rn)n1

The effective rate of interest reff that will produce the same interest per year as the rate of interest r compounded continuously is given by the formula:

reff=er1

Calculation:

Consider the nominal rate of interest r=5%.

First, consider the number of compounding per year to be 4.

Substitute r=0.05 and n=4 in the formula reff=(1+rn)n1,

reff=(1+rn)n1=(1+0.054)411.0509410.051

Hence, the effective rate of interest that will produce the same interest rate per year as nominal rate of interest r=5% compounded 4 times per year is 5.0945%.

Now, consider the number of compounding per year to be 12.

Substitute r=0.05 and n=12 in the formula reff=(1+rn)n1,

reff=(1+rn)n1=(1+0.0512)1211.0511610

(b)

To determine

To calculate: The effective rate of interest reff for the nominal rate of interest r=6% compounded 4, 12, 365 times and continuously and fill the following table:

 Number of compounding per year 4 12 365 Continuously Effective rate

(c)

To determine

To calculate: The effective rate of interest reff for the nominal rate of interest r=7.5% compounded 4,12,365 times and continuously and fill the following table:

 Number of compounding per year 4 12 365 Continuously Effective rate

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