Chapter B, Problem 18E

To determine

Concept introduction:

Present Value:

Present value of money means the present or current value of a future cash flow at a given rate of interest or return.

Future Value:

The future value is the value of present cash flow at specified time period and at specified rate of return.

Requirement 1:

We have to determine the amount to be deposited today.

Answer to Problem 18E

The amount to be deposited today will be $42480.

Explanation of Solution

$\begin{array}{l}\\ \text{Present value= FutureValue\&*\#x00A0;PVf(n,r)}\\ \text{Future value= 60,000}\\ \text{i= 9\%}\\ \text{n= 4 }\text{.}\\ \text{Present value = 60,000\&*\#x00A0;PV(4,9\%)}\\ \text{P= 42480}\end{array}$

To determine

Concept introduction:

Present Value:

Present value of money means the present or current value of a future cash flow at a given rate of interest or return.

Future Value:

The future value is the value of present cash flow at specified time period and at specified rate of return.

Requirement 2:

We have to determine the amount to be deposited today.

Answer to Problem 18E

The amount to be deposited today will be $12855

Explanation of Solution

$\begin{array}{l}\\ \text{Present value= FutureValue\&*\#x00A0;PVf(n,r)}\\ \text{Future value= 15,000}\\ \text{i= 8\%}\\ \text{n= 2 }\text{.}\\ \text{Present value = 15,000\&*\#x00A0;PV(2,8\%)}\\ \text{P= 12855}\end{array}$

To determine

Concept introduction:

Present Value:

Present value of money means the present or current value of a future cash flow at a given rate of interest or return.

Future Value:

The future value is the value of present cash flow at specified time period and at specified rate of return.

Requirement 3:

We have to determine the best option among the two.

Answer to Problem 18E

We will have $463 now as the future value of $463 after 10 years will be $1096.1062 which is greater than $1000.

Explanation of Solution

$\begin{array}{l}\text{Future value= PV\&*\#x00A0;FVf(n,r)}\\ \text{A= 463}\\ \text{i= 9\%}\\ \text{n= 10 }\text{.}\\ \text{Future value= 463\&*\#x00A0;Fvf(10,9\%)}\\ \text{P= 463*2}\text{.3674}\\ =\text{1096}\text{.1062}\end{array}$

We will have $463 now as the future value of $463 after 10 years will be $1096.1062 which is greater than $1000.

To determine

Concept introduction:

Present Value:

Present value of money means the present or current value of a future cash flow at a given rate of interest or return.

Future Value:

The future value is the value of present cash flow at specified time period and at specified rate of return.

Requirement 4:

We have to determine the cost of sticker in eight years.

Answer to Problem 18E

The cost of sticker in eight years will be $132.975

Explanation of Solution

$\begin{array}{l}\text{Future value= PV\&*\#x00A0;FVf(n,r)}\\ \text{A= 90}\\ \text{i= 5\%}\\ \text{n= 8}\text{.}\\ \text{Future value= 90\&*\#x00A0;Fvf(8,5\%)}\\ \text{P= 90*1}\text{.4775}\\ =\text{132}\text{.975}\end{array}$

To determine

Concept introduction:

Present Value:

Present value of money means the present or current value of a future cash flow at a given rate of interest or return.

Future Value:

The future value is the value of present cash flow at specified time period and at specified rate of return.

Requirement 5:

We have to determine the cost of new home after eight years.

Answer to Problem 18E

The cost of new home after eight years will be $339,760.60

Explanation of Solution

$\begin{array}{l}\text{Future value= PV\&*\#x00A0;FVf(n,r)}\\ \text{A= 158,500}\\ \text{i= 10\%}\\ \text{n= 8}\text{.}\\ \text{Future value= 158,500\&*\#x00A0;Fvf(8,10\%)}\\ \text{P= 158,500*2}\text{.1436}\\ =\text{339,760}\text{.60}\end{array}$

To determine

Concept introduction:

Present Value:

Present value of money means the present or current value of a future cash flow at a given rate of interest or return.

Future Value:

The future value is the value of present cash flow at specified time period and at specified rate of return.

Requirement 6:

We have to determine the amount of today’s investment.

Answer to Problem 18E

The amount of today’s investment will be $10852.32

Explanation of Solution

$\begin{array}{l}PV\text{ of single annuity }=\text{ AMT\&*\#x00A0;PVf(10,6\%)}\\ =10,000*0.558\\ \text{PV of single annuity }=\text{ \$5580}\\ \text{Interest annuity }=\text{ AMT\&*\#x00A0;PVoa (10,6\%)}\\ =\text{ 400*13}\text{.1808}\\ =\text{\$5272}\text{.32}\\ \text{Total Present Value }=\text{ \$10852}\text{.32}\\ \end{array}$

To determine

Concept introduction:

Present Value:

Present value of money means the present or current value of a future cash flow at a given rate of interest or return.

Future Value:

The future value is the value of present cash flow at specified time period and at specified rate of return.

Requirement 7:

We have to determine the present value of given situation.

Answer to Problem 18E

The present value of amount will be $5,734,500

Explanation of Solution

$\begin{array}{l}\text{Amount}=\text{ annual payment*PVoa(20,6\%)}\\ \text{A= 500,000}\\ \text{i= 6\%}\\ \text{n= 20}\\ \text{Amount= 500,000*11}\text{.469}\\ =\text{\$5,734,500}\end{array}$