Chapter 3, Problem 1RE

In Problems $1\text{-}4$, find the indicated quantity, given $A=P\left(1+rt\right)$.

$A=?;P=\text{\$}100;r=9\%;t=6\text{months}$

To determine

To calculate: The amount $A$ using compound interest formula, where, $P=\text{\$1}00,r=9\text{\%}$ and $t=6$ months.

Answer to Problem 1RE

The amount $A$ using compound interest formula, where, $P=\text{\$1}00,r=9\text{\%}$ and $t=6$ months is $\text{\$}104.50$.

Explanation of Solution

Calculation:

Consider the provided data,

$P=\text{\$1}00,r=9\text{\%}$ and $t=6$ months

Convert the months to years by dividing the value by 12,

$\begin{array}{c}t=\frac{6}{12}\\ =\frac{1}{2}\text{ years}\end{array}$

The formula for compound interest is,

$A=P\left(1+rt\right)$ …… (1)

In the formula, $A$ is the amount, $P$ is the principal, $r$ is the rate of interest and $t$ is the number of years.

So, substitute 100 for $P$, $0.09$ for $r$ and $\frac{1}{2}$ for $t$ in the equation (1),

$\begin{array}{c}A=100\left(1+\left(0.09\right)\left(\frac{1}{2}\right)\right)\\ =100\left(1+0.045\right)\\ =100\left(1.045\right)\\ =104.50\end{array}$

Hence, the value of $A$ using the formula for compound interest is $\text{\$}104.50$.