Chapter 10, Problem 1ECP

To determine

The simple interest and the maturity value for the amount $7,800 at $4\frac{1}{4}$% for 18 months.

Answer to Problem 1ECP

The simple interest and the maturity value for the amount $7,800 at $4\frac{1}{4}$% for 18 months are $497.25 and $8297.25, respectively.

Explanation of Solution

Given:

The principal amount (P) is $7,800.

The rate of interest (R) is $4\frac{1}{4}$% and time (T) is 18 months.

Formula used:

Simple interest:

Simple interest formula is $I=PRT$, where P is the principal amount, R is the rate of interest and T is the time.

Maturity value:

The maturity value is calculated using $MV=P+I$, where MV is the maturity value and I is the simple interest.

Calculation:

Compute the simple interest as follows.

Convert the rate of interest in to decimal as below.

$\begin{array}{c}R=4\frac{1}{4}\%\\ =\frac{17}{4}\left(\frac{1}{100}\right)\\ =\frac{17}{400}\\ =0.0425\end{array}$

Convert the 18 months into years.

$\begin{array}{c}T=18\text{ months}\\ \text{=}\frac{18}{12}\left[\because 1\text{ year = 12 months}\right]\end{array}$

Now substitute $P=7,800,R=0.0425\text{ and }T=\frac{18}{12}$ in $I=PRT$.

$\begin{array}{c}I=7,800\times 0.0425\times \frac{18}{12}\\ =7,800\times 0.06375\\ =497.25\end{array}$

Thus, the simple interest for the amount $7,800 at $4\frac{1}{4}$% for 18 months is $497.25.

Compute the maturity value as follows.

Substitute $I=497.25$ in $MV=P+I$.

$\begin{array}{c}MV=7,800+497.25\\ =8297.25\end{array}$

Thus, maturity value for the amount $7,800 at the $4\frac{1}{4}$% for 18 months is $8297.25.