Question

What annual installment will discharge a debt of Rs$1092$ due in $3$years at $12\%$ simple interest ?

Answer 1

Determine the annual installment will discharge a debt of Rs$1092$ due in $3$years at $12\%$ simple interest.

Simple Interest: A principal amount of the loan or the first deposit in a savings account is being used to compute the simple interest.

Formula:

$(S.I)=\frac{P\times R\times T}{100}$

Let the required annual installment be$\mathrm{Rs}.x$.

The calculated equation for the first year is equal to the sum of installment and interest of the remaining two years is as follows:

$\left[x+\frac{(x\times 12\times 2)}{100}\right]$

The calculated equation for the second year is equal to the sum of installment and interest of the remaining one year is as follows:

$\left[x+\frac{(x\times 12\times 1)}{100}\right]$

The calculated equation for the third year is equal to installment only as no other year remained is $x$

Now Since all the above equations sum total to give the debt discharged,

Hence, the equation obtained to calculate the required installment is as follows:

$\begin{array}{rcl}& \Rightarrow & \left[x+\frac{\left(x\times 12\times 2\right)}{100}\right]+\left[x+\frac{\left(x\times 12\times 1\right)}{100}\right]+x=1092\\ & \Rightarrow & 3x+\left(\frac{24x}{100}\right)+\left(\frac{12x}{100}\right)=1092\\ & \Rightarrow & \frac{336x}{100}=1092\\ & \Rightarrow & 336x=109200\\ & \Rightarrow & x=325\end{array}$

Hence, $\mathrm{Rs}.325$ is the annual installment that will discharge a debt of $\mathrm{Rs}.1092$ due in $3$years at $12\%$ simple interest.