Chapter 7.7, Problem 15E

Solution

1.

To calculate: the time of simple interest when $\text{Balance}(A)=\$5000,\text{Principal(}P)=\$4000,$

  $\text{interest}\text{rate(r)=5\% simple interest per year}$

Time of simple interest is 13 $5\text{years}$

Given information:

  $\text{Balance}(A)=\$5000,\text{Principal(}P)=\$4000,\text{interest}\text{rate(r)=5\% simple interest per year}$

Concept Used:

Simple interest problem requires the use of the following formula:

  $\begin{array}{l}I=Prt\\ A=P+I\end{array}$

Calculation:

As per the given problem

  $\text{Balance}(A)=\$5000,\text{Principal(}P)=\$4000,\text{interest}\text{rate(r)=5\% simple interest per year}$

Substitute the values in the formula

  $\begin{array}{l}A=P+I\\ \Rightarrow 5000=4000+I\\ \Rightarrow I=5000-4000\\ \Rightarrow I=1000\end{array}$

  $\begin{array}{l}I=Prt\\ \Rightarrow 1000=4000\times \frac{5}{100}\times t\\ \Rightarrow t=\frac{1000}{200}\\ \Rightarrow t=5\text{years}\end{array}$

Time of simple interest is $5\text{years}$

Conclusion:

Time of simple interest is $5\text{years}$

2.

To calculate:

The principal amount when $\text{Balance}(A)=\$11,160,\text{interest}\text{rate(r)=8\% simple interest per year}$

  $\text{and}\text{time}(t)=36\text{months}$

The principal amount is $\$9000$

Given information: $\text{Balance}(A)=\$11,160,\text{interest}\text{rate(r)=8\% simple interest per year}$

  $\text{and}\text{time}(t)=36\text{months=3years}$

Concept Used:

Simple interest problem requires the use of the following formula:

  $\begin{array}{l}I=Prt\\ A=P+I\end{array}$

Calculation:

As per the given problem,

  $\text{Balance}(A)=\$11,160$ , $\text{interest}\text{rate(r)=8\%}$ simple interest per year and time $(t)$

  $=36\text{months}$

  $=3\text{years}$

Substitute the values in the formula

  $\begin{array}{l}I=Prt\\ \Rightarrow I=P\times \frac{8}{100}\times 3\\ \Rightarrow I=\frac{24P}{100}\end{array}$

  $\begin{array}{l}A=P+I\\ \Rightarrow 11160=P+\frac{24P}{100}\\ \Rightarrow 11160=\frac{124P}{100}\\ \Rightarrow P=\frac{11160\times 100}{124}\\ \Rightarrow P=9000\end{array}$

The principal amount is $\$9000$

Conclusion:

The principal amount is $\$9000$

3.

To calculate:

The Interest rate $(r)$ when $\text{Balance}(A)=\$3207,\text{Principal(}P)=\$3000,\text{and}\text{time}(t)=18\text{months}$

The rate of interest is $\text{4}\text{.6\%}\text{simple}\text{interest}\text{per}\text{year}$

Given information: $\text{Balance}(A)=\$3207,\text{Principal(}P)=\$3000,\text{and}\text{time}(t)=18\text{months}$

Concept Used:

Simple interest problem requires the use of the following formula:

  $\begin{array}{l}I=Prt\\ A=P+I\end{array}$

Calculation:

As per the given problem,

  $\text{Balance}(A)=\$3207,\text{Principal(}P)=\$3000,\text{and}\text{time}(t)=18\text{months=}\frac{3}{2}\text{year}$

Substitute the values in the formula

  $\begin{array}{l}A=P+I\\ \Rightarrow 3207=3000+I\\ \Rightarrow I=3207-3000\\ \Rightarrow I=207\end{array}$

  $\begin{array}{l}I=Prt\\ \Rightarrow 207=3000\times \frac{r}{100}\times \frac{3}{2}\\ \Rightarrow r=\frac{207\times 2}{90}\\ \Rightarrow r=4.6\%\end{array}$

The rate of interest is $\text{4}\text{.6\%}\text{simple}\text{interest}\text{per}\text{year}$

Conclusion:

The rate of interest is $\text{4}\text{.6\%}\text{simple}\text{interest}\text{per}\text{year}$