Chapter 5, Problem 1RE

To determine

To calculate: The value of simple interest on the given loan.

Answer to Problem 1RE

Solution: $\underset{\_}{\$292.08}$

Explanation of Solution

Given: The principal (P) value of loan is $\$4902$, the rate (r) of interest is $6.5\%,$ and the time (t) is $11$ months.

Formula Used:

$I=P\times r\times t$, where ‘P’ be the principal amount, ‘r’ be the rate of interest and ‘t’ be the number of year.

Calculation:

Step 1: Rate is expressed as a decimal while calculating the interest. Thus, to convert the rate percent into a decimal, rate percent is divided by 100.

$\begin{array}{ccc}\hfill r& =& 6.5\%\hfill \\ \hfill & =& \frac{6.5}{100}\hfill \\ \hfill & =& 0.065\hfill \end{array}$

Step 2: The time is to be expressed in year. Thus, to convert the time into the year, the months are divided by 12.

$\begin{array}{ccc}\hfill t& =& \frac{\text{11 months}}{12\text{ months}}\hfill \\ \hfill & =& \frac{11}{12}\hfill \end{array}$

Step 3: The interest is computed by multiplying the principal amount by rate and time. Thus, in order to calculate the interest, apply this formula:

$\begin{array}{ccc}\hfill I& =& P\times r\times t\hfill \\ \hfill & =& \$4902\times 0.065\times \frac{11}{12}\hfill \\ \hfill & =& \$292.08\hfill \end{array}$

Therefore, the simple interest on the loan of $\$4902$ is $\underset{\_}{\$292.08}$.