Chapter SH, Problem 1.7EP

To determine

To find:the interest of an investment after 3 years.

Answer to Problem 1.7EP

  $I=\$551.6875$ .

Explanation of Solution

Given:

The given formulafor compound interest is $A=P{\left(1+r\right)}^t$ .

The principle amount, rate of interest and time period is given below:

  $P=\$3500,r=5\%,t=3$ .

Calculation:

As the formula for compound interest is $A=P{\left(1+r\right)}^t$ .

Now, substitutes the principle amount, rate of interest and time period in the above formula. Therefore,

  $\begin{array}{l}A=P{\left(1+r\right)}^t\{\text{given}}\\ A=3500{\left(1+5\%\right)}^3\text{{substitutes these value}}\\ A=3500{\left(1+\frac{5}{100}\right)}^3\text{{simplify}\}\\ A=3500{\left(1+0.05\right)}^3\{\text{simplify}}\\ A=3500{\left(1.05\right)}^3\{\text{simplify}}\\ A=3500\times 1.57\{\text{simplify}}\\ A=4051.6875\end{array}$

Thus, the amount after 3 years of an investment is $A=4051.6875$ .

Therefore, the interest gain by the investment is

  $\begin{array}{l}I=A-P\\ =\$4051.6875-3500\\ =\$551.6875\end{array}$

Hence,the interest of an investment after 3 yearsis $I=\$551.6875$ .