Exercise 17 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 $900 in a savings account with we earn $54 simple interest in 18 months. We want to calculate the annual rate. Keep in mind that 18 months represents 1812 years. P= 900, I= 54, t= 18/12 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

54=( 900)( r)( 18/12)

MultEqn

LHS * 12=RHS* 12

54* 12 = (900)( r)(18/12)* 12

FracMultDenomToNumber

a/12* 12 = a

54* 12 = (900)( r)(18)

DivEqn

.LHS /(900)(18).=.RHS /(900)(18).

54* 12/(900)(18)=(900)( r)(18)/(900)(18)

CancelCommonFac

Cancel out common factors

54* 12/(900)(18)=(900)( r)(18)/(900)(18)

SimpQuot

Simplify quotient

54* 12/(900)(18)= r

Multiply

Multiply

648/16 200= r

CalcQuot

Calculate quotient

0.04= r

RearrangeEqn

Rearrange equation

r=0.04

Since the decimal number 0.04 is equal to 4%, the annual interest rate is 4%.