Chapter 5, Problem 1CE

(a)

To determine

To calculate: Compound Amount for the investment.

Answer to Problem 1CE

Solution:

$\underset{\_}{\$22,550}$.

Explanation of Solution

Given:

An amount of $20,000 $\left(P\right)$ is compounded continuously for the period of 2 years(n) and the rate of interest is 6% $\left(i\right)$.

Formula used: $A=P{e}^{rt}$

Calculation:

To compute the compound amount of the deposit whose principal amount is $20,000 and is compounded daily. The rate of interest is 6% and a number of years (n) is 2 years following formula should be used:

$A=P{e}^{rt}$

where, $A$ is compounding amount $\left(P\right)$ is Principal $r$ is rate $t$ is time or number of years.

Now, using above formula:

$\begin{array}{ccc}\hfill A& =& P{e}^{rt}\hfill \\ \hfill & =& \$20,000\times e^{0.06\times 2}\hfill \\ \hfill & =& \$20,000\times e^{0.12}\hfill \end{array}$

Further calculation of equation:

$\begin{array}{ccc}\hfill A& =& \$20,000\times 1.127497\hfill \\ \hfill & =& \$22,549.94\hfill \\ \hfill & \approx & \$22,550\hfill \end{array}$

Thus, the compound amount is $22,550.

(b)

To determine

To calculate: Compound Amount for the investment.

Answer to Problem 1CE

Solution:

$\underset{\_}{\$36,442.38}$.

Explanation of Solution

Given:

An amount of $20,000 $\left(P\right)$ is compounded continuously for the period of 10 years(n) and the rate of interest is 6% (i).

Formula used: $A=P{e}^{rt}$

Calculation:

To compute the compound amount of the deposit whose principal amount is $20,000 and is compounded daily. The rate of interest is 6% and number of years $\left(n\right)$ is 10 years following formula should be used.

$A=P{e}^{rt}$

where, $A$ is compounding amount $\left(P\right)$ is Principal $r$ is rate $t$ is time or number of years.

Now, using above formula:

$\begin{array}{ccc}\hfill A& =& P{e}^{rt}\hfill \\ & =& \$20,000\times e^{0.06\times 10}\hfill \\ \hfill & =& \$20,000\times e^{0.6}\hfill \end{array}$

Further calculation of equation:

$\begin{array}{ccc}\hfill A& =& \$20,000\times 1.8221188\hfill \\ \hfill & =& \$36,442.38\hfill \end{array}$

Thus, the compound amount is $\$36,442.38$.

(c)

To determine

To calculate: Compound Amount for the investment.

Answer to Problem 1CE

Solution:

$\underset{\_}{\$66,402.34}$

Explanation of Solution

Given:

An amount of $20,000 $\left(P\right)$ is compounded continuously for the period of 20 years $\left(n\right)$ and the rate of interest is 6% (i).

Formula used: $A=P{e}^{rt}$

Calculation:

To compute the compound amount of the deposit whose principal amount is $20,000 and is compounded daily. The rate of interest is 6% and number of years $\left(n\right)$ is 10 years following formula should be used.

$A=P{e}^{rt}$

where, $A$ is compounding amount $\left(P\right)$ is Principal $r$ is rate $t$ is time or number of years.

Now, using above formula:

$\begin{array}{ccc}\hfill A& =& P{e}^{rt}\hfill \\ \hfill & =& \$20,000\times e^{0.06\times 20}\hfill \\ \hfill & =& \$20,000\times e^{1.2}\hfill \end{array}$

Further calculation of equation:

$\begin{array}{ccc}\hfill A& =& \$20,000\times 3.3201169\hfill \\ \hfill & =& \$66,402.34\hfill \end{array}$

Thus, the compound amount is $\$66,402.34$.