Chapter 8.3, Problem 50PPE

(a)

To determine

To rewrite: The equation in standard form.

Answer to Problem 50PPE

The standard form is $1500{(1+r)}^3=1500r^3+4500r^2+4500r+1500$

Explanation of Solution

Given information:

Value of account: $1500{(1+r)}^3$

  $1500{(1+r)}^3=1500(1+r)(1+r)(1+r)$

Calculation:

The standard form of equation is:

  $\begin{array}{}$ 1500{(1+r)}^3=1500(1+r)(1+r)(1+r)$$ 1500{(1+r)}^3=1500(1+2r+r^2)(1+r)$$ 1500{(1+r)}^3=1500[1(1+r)+2r(1+r)+r^2(1+r)]$$ 1500{(1+r)}^3=1500(1+r+2r+2r^2+r^2+r^3)$$ 1500{(1+r)}^3=1500(r^3+3r^2+3r+1)$$ 1500{(1+r)}^3=1500r^3+4500r^2+4500r+1500$\end{array}$

Conclusion:

The standard form is $1500{(1+r)}^3=1500r^3+4500r^2+4500r+1500$

(b)

To determine

To find: The Money in the account after three year when interest rate is 3%.

Answer to Problem 50PPE

$96,000 will be in the account after three year when interest rate is 3%.

Explanation of Solution

Given information:

Value of account:

Calculation:

Value of account: $1500{(1+r)}^3$

  $\begin{array}{l}$ 1500{(1+r)}^3$$ 1500{(1+3)}^3$$ 1500{(4)}^3$\$96,000\end{array}$

Conclusion:

$96,000 will be in the account after three year when interest rate is 3%.