Chapter 16, Problem 14FPP

Summary Introduction

a.

To determine:

Total amount invested at the end of four years.

Introduction: Total amount invested is the amount of total investment during given period of time.

Answer to Problem 14FPP

Solution:

Total amount invested during last four years is $12,000.

Explanation of Solution

Given,

Amount invested in 2010 is $3,000.

Amount invested in 2011 is $3,000.

Amount invested in 2012 is $3,000.

Amount invested in 2013 is $3,000.

Formula to calculate total amount invested is as follows:

$\text{Total amount invested}=\text{Amount invested in }(2010+2011+2012+2013)$

Substitute $3000 for the amount invested in 2010, $3000 for the amount invested in 2011, $3000 for the amount invested in 2012, $3000 for the amount invested in 2013.

$\begin{array}{c}\text{Total amount invested}=\$3,000+\$3,000+\$3,000+\$3,000\\ =\$12,000\end{array}$

Summary Introduction

b.

To determine:

Total number of mutual fund shares purchased.

Introduction: Professionally controlled investment scheme run by asset management company that bring group of people together to invest in securities, stocks and bonds is known as mutual funds.

Answer to Problem 14FPP

Solution:

Total number of mutual fund shares purchased is $273.10.

Explanation of Solution

given,

Amount invested in 2010 is $3,000.

Amount invested in 2011 is $3,000.

Amount invested in 2012 is $3,000.

Amount invested in 2013 is $3,000.

Price per share in 2010 is $40 per share.

Price per share in 2011 is $45 per share.

Price per share in 2012 is $42 per share.

Price per share in 2013 is $50 per share.

Formula to calculate total number of mutual fund shares purchased is as follows:

$\text{Total number of shares purchased}=\text{Shares purchased in}\left(2010+2011+2012+2013\right)$

Substitute 75 for number of shares purchased in 2010, 66.67 for number of shares purchased in 2011, 71.43 for number of shares purchased in 2012, 60 for number of shares purchased in 2013 (calculated in working note).

$\begin{array}{c}\\ \text{Total number of shares purchased}=75+66.67+71.43+60\\ =273.10\end{array}$

Working Note:

Formula to calculate number of shares in 2010 is as follows:

$\text{Number of shares in 2010}=\frac{\text{Amount invested}}{\text{Price per share}}$

Substitute $3,000 for amount invested and $40 for price per share.

$\begin{array}{c}\text{Number of shares in 2010}=\frac{\$3,000}{\$40}\\ =75\end{array}$

Formula to calculate number of shares in 2011 is as follows:

$\text{Number of shares in 2011}=\frac{\text{Amount invested}}{\text{Price per share}}$

Substitute $3,000 for amount invested and $45 for price per share.

$\begin{array}{c}\text{Number of shares in 2011}=\frac{\$3,000}{\$45}\\ =66.67\end{array}$

Formula to calculate number of shares in 2012 is as follows:

$\text{Number of shares in 2012}=\frac{\text{Amount invested}}{\text{Price per share}}$

Substitute $3,000 for amount invested and $42 for price per share.

$\begin{array}{c}\text{Number of shares in 2012}=\frac{\$3,000}{\$42}\\ =71.43\end{array}$

Formula to calculate number of shares in 2013 is as follows:

$\text{Number of shares in 2013}=\frac{\text{Amount invested}}{\text{Price per share}}$

Substitute $3,000 for amount invested and $50 for price per share.

$\begin{array}{c}\text{Number of shares in 2013}=\frac{\$3,000}{\$50}\\ =60\end{array}$

Summary Introduction

c.

To determine:

The average cost for each mutual fund share at the end of four years.

Introduction: Total amount invested is the amount of total investment during given period of time.

Answer to Problem 14FPP

Solution:

The average cost of each mutual fund share is $43.94.

Explanation of Solution

Given,

Total amount invested is $12,000 (calculated in part a)

Total number of shares purchased is 273.10 (calculated in part b).

Formula to calculate average cost of each mutual fund is as follows:

$\text{Average cost of each mutual fund share}=\frac{\text{Total investments}}{\text{Total number of shares purchased}}$

Substitute $12,000 for total investment and 273.10 for total number of shares purchased in the above formula,

$\begin{array}{c}\text{Average cost of each mutual fund share}=\frac{\$12,000}{273.10}\\ =\$43.94\end{array}$