Chapter 6.6, Problem 31IP

To determine

To find: What will be amount of the fifth bill and seventh bill.

Answer to Problem 31IP

Amount of Fifth bill $=\$137.77$

Amount of Seventh bill $=\$39.68$

Explanation of Solution

Given information:

The table shows the first three monthly bills.

New balance after three months is Principal amount of Fourth month.

Therefore,For Fourth monthPrincipal amount $=p=\$182.99$

Interest rate $=r=1.5\%=0.015$

Time $=t=1$ year

Time will be 1 year because for compound interest we need to calculate separately for every year.

We know

  $I=prt$

On substituting values

We get

  $\begin{array}{l}I=prt\\ \Rightarrow I=\left(182.99\right)\left(0.015\right)\left(1\right)\\ \Rightarrow I=2.74\end{array}$

Therefore,

Total amount that is Bill amount of fourth month $=$ Principal amount $+$interest

Total amount that is Bill amount of fourth month $=$$182.99+2.74=\$185.73$

Bill Amount of Fourth Month $=\$185.73$

As every Month James makes a payment of $\$50$

New balance $=$Bill amount $-$Payment

$\Rightarrow$New balance $=$$185.73-50$

$\Rightarrow$New balance at end of fourth month$=$$135.73$

New balance after four months is Principal amount of Fifth month.

Therefore,

For Fifth month

Principal amount $=p=\$135.73$

Interest rate $=r=1.5\%=0.015$

Time $=t=1$ year

Time will be 1 year because for compound interest we need to calculate separately for every year.

We know

  $I=prt$

On substituting values

We get

  $\begin{array}{l}I=prt\\ \Rightarrow I=\left(135.73\right)\left(0.015\right)\left(1\right)\\ \Rightarrow I=2.04\end{array}$

Therefore,

Total amount that is Bill amount of fifth month $=$Principal amount $+$ interest

Total amount that is Bill amount of fifth month $=$$135.73+2.04=\$137.77$

Bill Amount of Fifth Month $=\$137.77$

As every Month James makes a payment of$\$50$

New balance $=$Bill amount $-$Payment

$\Rightarrow$New balance $=$$137.77-50$

$\Rightarrow$New balance at end of fifth month $=$$\$87.77$

New balance after five months is Principal amount of Sixth month.

Therefore,For Sixth monthPrincipal amount $=p=\$87.77$

Interest rate $=r=1.5\%=0.015$

Time $=t=1$year

Time will be 1 year because for compound interest we need to calculate separately for every year.

We know

  $I=prt$

On substituting values

We get

  $\begin{array}{l}I=prt\\ \Rightarrow I=\left(87.77\right)\left(0.015\right)\left(1\right)\\ \Rightarrow I=1.32\end{array}$

Therefore,

Total amount that is Bill amount of sixth month $=$Principal amount $+$ interest

Total amount that is Bill amount of sixth month $=$$87.77+1.32=\$89.09$

Bill Amount of Sixth Month $=\$89.09$

As every Month James makes a payment of$\$50$

New balance $=$Bill amount $-$Payment

$\Rightarrow$New balance $=$$89.09-50$

$\Rightarrow$New balance at end of Sixth month $=$$\$39.09$

New balance after six months is Principal amount of Seventh month.

Therefore,For Seventh monthPrincipal amount $=p=\$39.09$

Interest rate $=r=1.5\%=0.015$

Time $=t=1$ year

Time will be 1 year because for compound interest we need to calculate separately for every year.

We know

  $I=prt$

On substituting values

We get

  $\begin{array}{l}I=prt\\ \Rightarrow I=\left(39.09\right)\left(0.015\right)\left(1\right)\\ \Rightarrow I=0.59\end{array}$

Therefore,

Total amount that is Bill amount of seventh month $=$Principal amount $+$interest

Total amount that is Bill amount of seventh month $=$$39.09+0.59=\$39.68$

Bill Amount of Seventh Month $=\$39.68$

Therefore,Amount of Fifth bill $=\$137.77$

Amount of Seventh bill $=\$39.68$