Exercise 24 Page 270

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 $400 in a savings account with we earn $18 simple interest in 9 months. We want to calculate the annual rate. Keep in mind that 9 months represents 912 years. P= 400, I= 18, t= 9/12 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

18=( 400)( r)( 9/12)

MultEqn

LHS * 12=RHS* 12

18* 12 = (400)( r)(9/12)* 12

FracMultDenomToNumber

a/12* 12 = a

18* 12 = (400)( r)(9)

DivEqn

.LHS /(400)(9).=.RHS /(400)(9).

18* 12/(400)(9)=(400)( r)(9)/(400)(9)

CancelCommonFac

Cancel out common factors

18* 12/(400)(9)=(400)( r)(9)/(400)(9)

SimpQuot

Simplify quotient

18* 12/(400)(9)= r

Multiply

Multiply

216/3600= r

CalcQuot

Calculate quotient

0.06= r

RearrangeEqn

Rearrange equation

r=0.06

Since the decimal number 0.06 is equal to 6%, the annual interest rate is 6%.