Chapter 8, Problem 9PT

a.

To determine

To find: Explain the numbers in this expression.

Explanation of Solution

Given information:

Total amount of money after two years is calculated by an expression $4000{\left(1+0.05\right)}^2$

Given

Total amount of money after two years is calculated by an expression $4000{\left(1+0.05\right)}^2$

Here

Using formula of compound interest

We get

  $4000$ is the principal amount

  $0.05$ is the interest rate in factor form

  $2$ is the number of years.

b.

To determine

To find: Amount at the end of two years.

Answer to Problem 9PT

Total amount after two years $=\$4410$

Explanation of Solution

Given information:

Total amount of money after two years is calculated by an expression $4000{\left(1+0.05\right)}^2$

Given

Total amount of money after two years is calculated by an expression $4000{\left(1+0.05\right)}^2$

On solving

We get

Total amount $=4000{\left(1+0.05\right)}^2$

  $\Rightarrow$ Total amount $=4000{\left(1.05\right)}^2$

  $\Rightarrow$ Total amount $=4000\left(1.1025\right)$

  $\Rightarrow$ Total amount $=\$4410$

Therefore,

Total amount after two years $=\$4410$

c.

To determine

To find: Amount at the end of four years.

Answer to Problem 9PT

Total amount after four years $=\$5097.7$

Explanation of Solution

Given information:

Time $=4$ years

Interest rate $=6.25\%=0.0625$

Given

We know

  $4000$ is the principal amount

And given

Time $=4$ years

Interest rate $=6.25\%=0.0625$

On substituting values

We get

Total amount $=4000{\left(1+0.0625\right)}^4$

  $\Rightarrow$ Total amount $=4000{\left(1.0625\right)}^4$

  $\Rightarrow$ Total amount $=4000\left(1.2744\right)$

  $\Rightarrow$ Total amount $=\$5097.7$

Therefore,

Total amount after four years $=\$5097.7$