Problem 5.07 (Excel Video) Find the future value of a five-year $101,000 investm

Question

Problem 5.07 (Excel Video) Find the future value of a five-year $101,000 investment that pays 8.25 percent and that has the following compounding periods: (Do not round intermediate calculations, round final answers to 2 decimal places, e.g. 15.25.) Excel Template (Note: This template includes the problem statement as it appears in your textbook. The problem assigned to you here may have different values. When using this template, copy the problem statement from this screen for easy reference to the values you've been given here, and be sure to update any values that may have been pre-entered in the template based on the textbook version of the problem.) Value of investment after 5 years a. Quarterly b. Monthly c. Daily d. Continuous Click if you would like to Show Work for this question:

Explanation / Answer

Solution:

The future value of an Investment after compounding for a given no. of periods including the interest is calculated as follows:

FV = P ( 1 + (r/n) )nt

Where

FV = Future value of investment including compound Interest

P = Principal amount invested

r = annual rate of interest

n = number of times the interest is compounded per year

t = number of years for which the investment is made

a. Value of Investment after 5 Years with Quarterly compounding:

As per the information given in the question we have

P = $ 101,000   ; r = 8.25 % ; n = quarterly = 4     ; t = 5 years

Applying the above values in the formula we have

FV = $ 101,000 ( 1 + (0.0825 / 4))4*5

       = $ 101,000 ( 1 + (0.0206))20 =   $ 101,000 ( 1.0206 )20

        = $ 101,000 * 1.504264

     = $ 151,930.66

Thus the Value of Investment after 5 Years with Quarterly compounding at 8.25 % interest rate = $ 151,930.66

Note : The value of ( 1.0206 )20 has been calculated using the excel formula

=POWER(Number,Power) = POWER(1.0206,20)

b. Value of Investment after 5 Years with Monthly compounding:

As per the information given in the question we have

P = $ 101,000   ; r = 8.25 % ; n = monthly = 12    ; t = 5 years

Applying the above values in the formula we have

FV = $ 101,000 ( 1 + (0.0825 / 12))12*5

       = $ 101,000 ( 1 + (0.0069))60 =   $ 101,000 ( 1.0069 )60

        = $ 101,000 * 1.508459

     = $ 152,354.34

Thus the Value of Investment after 5 Years with Monthly compounding at 8.25 % interest rate = $ 152,354.34

Note : The value of ( 1.0069 )60 has been calculated using the excel formula

=POWER(Number,Power) = POWER(1.0069,60)

c. Value of Investment after 5 Years with Daily compounding:

As per the information given in the question we have

P = $ 101,000   ; r = 8.25 % ; n = daily = 365    ; t = 5 years

Applying the above values in the formula we have

FV = $ 101,000 ( 1 + (0.0825 / 365))365*5

       = $ 101,000 ( 1 + (0.0002))1825 =   $ 101,000 ( 1.0002 )1825

        = $ 101,000 * 1.510519

     = $ 152,562.43

Thus the Value of Investment after 5 Years with daily compounding at 8.25 % interest rate = $ 152,562.43

Note : The value of ( 1.0002 )1825 has been calculated using the excel formula

=POWER(Number,Power) = POWER(1.0002,1825)

d. Value of Investment after 5 Years with Continuous compounding:        

The formula for calculating the Future value of an Investment with continuous compounding is as follows :

FV = P * ert    Where,

FV = Future value of the investment

P = Principal amount of investment

e =Mathematical constant = 2.71828

r = annual rate of interest

t = number of years for which the investment is made

As per the information given in the question we have

P = $ 101,000   ; r = 8.25 %   ; t = 5 years

Applying the above values in the formula we have

FV = $ 101,000 * ( 2.71828 )( 0.0825 * 5 )

         = $ 101,000 * ( 2.71828 )0.4125

     = $ 101,000 * 1.510589

     = $ 152,569.50

Thus the Value of Investment after 5 Years with continuous compounding at 8.25 % interest rate = $ 152,569.50

Note : The value of ( 2.71828 )0.4125 has been calculated using the excel formula

=POWER(Number,Power) = POWER(2.71828,0.4125)

The final solution is as follows:

a. Quarterly = $ 151,930.66

b. Monthly = $ 152,354.34

c. Daily   = $ 152,562.43

d. Continuous = $ 152,569.50

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