Fundamentals of Corporate Finance Standard Edition
Fundamentals of Corporate Finance Standard Edition
10th Edition
ISBN: 9780078034633
Author: Stephen Ross, Randolph Westerfield, Bradford D. Jordan
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 5, Problem 5QP
Summary Introduction

To determine: The number of periods of investment

Introduction:

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. The value increases based on the period of investment. The value of the investment will be higher if the duration of investment is longer.

Expert Solution & Answer
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Answer to Problem 5QP

The number of periods is as follows:

Particulars

Present

value

Years

Interest

Rate

Future

value

Investment A $560 10.35 9% $1,389
Investment B $810 8.46 10% $1,821
Investment C $18,400 17.56 17% $289,715
Investment D $21,500 21.44 15% $430,258

Explanation of Solution

Given information:

Investment A has a present value of $560, future value of $1,369, and an interest rate of 9 percent. Investment B has a present value of $810, future value of $1,821, and an interest rate of 10 percent.

Investment C has a present value of $18,400, future value of $289,715, and an interest rate of 17 percent. Investment D has a present value of $21,500, future value of $430,258, and an interest rate of 15 percent.

Formula:

Derive the formula to calculate the number of periods from the present value equation as follows:

PV=FV(1+r)t(1+r)t=FVPVln(1+r)t=ln(FVPV)

The power rule of naturallogarithm states that[ln(xy) = y× ln(x)] Hence,t×ln(1+r)=ln(FVPV)Divide the right hand side and left hand side byln(1+r)

t×ln(1+r)ln(1+r)=ln(FVPV)ln(1+r)t=ln(FVPV)ln(1+r)

The formula to calculate the number of periods:

t=ln(FVPV)ln(1+r)

Where,

“t” refers to the number of years or periods of investment

“ln” refers to the log value

“FV” refers to the future value

“PV” refers to the present value

“r” refers to the simple rate of interest

Compute the number of periods for Investment A:

t=ln($1,389$560)ln(1+0.09)=ln(2.44)ln(1.09)=10.35 years

Hence, the number of periods of Investment A is 10.35 years.

Compute the number of periods for Investment B:

t=ln($1,821$810)ln(1+0.10)=ln(2.24)ln(1.10)=8.46 years

Hence, the number of periods of Investment B is 8.46 years.

Compute the number of periods for Investment C:

t=ln($289,715$18,400)ln(1+0.17)=ln(15.75)ln(1.17)=17.56 years

Hence, the number of periods of Investment C is 17.56 years.

Compute the number of periods for Investment D:

t=ln($430,258$21,500)ln(1+0.15)=ln(20.01)ln(1.15)=21.44 years

Hence, the number of periods of Investment D is 21.44 years.

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