Exercise 18 Page 269

If we borrow money from a bank, we pay the bank interest for the use of their money. Similarly, if we open a savings account, the bank deposits extra money on this account as interest. To calculate the interest I, we use the simple interest formula. I= P r t, where... I& = Interest P& = Principal r& = Annual interest rate t& = Time (in years)We know that we deposit $2000 in a savings account with we earn $160 simple interest in 8 months. We want to calculate the annual rate. Keep in mind that 8 months represents 812 years. P= 2000, I= 160, t= 8/12 To calculate the interest, we will substitute these values into the simple interest formula and solve the resulting equation for r.

I=Prt

SubstituteValues

Substitute values

160=( 2000)( r)( 8/12)

MultEqn

LHS * 12=RHS* 12

160* 12 = (2000)( r)(8/12)* 12

FracMultDenomToNumber

a/12* 12 = a

160* 12 = (2000)( r)(8)

DivEqn

.LHS /(2000)(8).=.RHS /(2000)(8).

160* 12/(2000)(8)=(2000)( r)(8)/(2000)(8)

CancelCommonFac

Cancel out common factors

160* 12/(2000)(8)=(2000)( r)(8)/(2000)(8)

SimpQuot

Simplify quotient

160* 12/(2000)(8)= r

Multiply

Multiply

1920/16 000= r

CalcQuot

Calculate quotient

0.12= r

RearrangeEqn

Rearrange equation

r=0.12

Since the decimal number 0.12 is equal to 12%, the annual interest rate is 12%.