Chapter 9.3, Problem 6GP

Solution

(a)

The equation $A=p\left(1+r\right)$ for P .

  $p=\frac{A}{1+r}$

Given information:

The equation: $A=p\left(1+r\right)$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the formula for p , first divide each sides by (1+r ), to simplify further as shown below:

  $\begin{array}{l}A=p\left(1+r\right)\\ \frac{A}{1+r}=\frac{p\left(1+r\right)}{1+r}\\ \frac{A}{1+r}=p\\ p=\frac{A}{1+r}\end{array}$

Thus, the formula is $p=\frac{A}{1+r}$ .

(b)

To explain how to solve the equation for P.

The equation $A=p\left(1+r\right)$ .

In the given equation, A is the account balance, P is the principal and r is the interest rate. First divide the given equation by (1+ r ) to simplify the formula for the principal, that is P.

(c)

The equation $A=p\left(1+r\right)$ for r .

  $r=\frac{A-P}{P}$

Given information:

The equation: $A=p\left(1+r\right)$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the formula for r , first divide each sides by P, and then subtract 1 from both sides to simplify further as shown below:

  $\begin{array}{l}A=P\left(1+r\right)\\ \frac{A}{P}=\frac{P\left(1+r\right)}{P}\\ \frac{A}{P}=1+r\\ \frac{A}{P}-1=1-1+r\\ \frac{A-P}{P}=r\\ r=\frac{A-P}{P}\end{array}$

Thus, the formula is $r=\frac{A-P}{P}$ .

(d)

To explain how to solve the equation for r.

The equation $A=p\left(1+r\right)$ .

In the given equation, A is the account balance, P is the principal and r is the interest rate. First divide the given equation by P and then subtract 1 from both sides to simplify the formula for the interest rate , that is r.