Question

A sum of \[Rs.\ 550\] was taken as a loan. This is to be paid in two equal instalments. If the rate of interest is \[20\%\ \] compound annually. then the amount of each instalment will be
A). \[Rs.\ 360\]
B). \[Rs.\ 350\]
C). \[Rs.\ 340\]
D). \[Rs.\ 300\]

Answer 1

Hint: In this question, given that the sum of \[Rs.\ 5500\] was taken as a loan. Also given the rate of interest is \[20\%\ \]. Then we need to find the amount of each instalment. Also given that the loan needs to be paid in two instalments. By calculating the interest for both the years separately, we can calculate the amount of each instalment.
Formula used :
Simple interest,
 \[\S.I = \dfrac{\ P \times R \times T}{100}\]
Where,
         \[P\] is principal amount
         \[T\] is time period
         \[R\] is rate of interest

Complete step-by-step solution:
Given, \[{Principle\ }\left( P \right) = 550\]
\[Rate\ of\ interest\ = \ 20\%\]
\[R\ = \dfrac{20}{100}\]
By simplifying,
We get,
\[R = 0.2\]
Let \[x\] be instalment at the end of one year.
Now we need to find the interest for first year,
We need to find the interest,
\[Interest\ = \dfrac{{PTR}}{100}\]
By substituting the values,
We get,
\[I\ = \dfrac{\left( 550 \times 1 \times 20 \right)}{100}\]
By simplifying,
We get ,
\[I\ = \ 110\]
We have assumed that \[x\] needs to be paid as equal instalment.
Now, at the beginning of second year,
\[P = \ 550 + 110 – x\]
By simplifying,
We get,
\[P\ = \ 660 – x\]
Now interest at the end of second year,
\[I\ = \left( 660 – x \right) \times 0.2\]
By simplifying,
We get ,
 \[\ I = 132 – 0.2x\]
Now we need to find the total instalment,
For that we need to add both the instalments.
 \[x + x = 550 + 110 + 132 – 0.2x\]
By simplifying,
We get,
\[2x = 792 – 0.2x\]
\[2x + 0.2x = 792\]
By adding the variables,
We get,
\[2.2x = 792\]
\[\ x = \dfrac{792}{2.2}\]
By dividing,
We get,
\[x = \ 360\]
Thus the amount of each instalment be \[Rs.\ 360\]
Final answer :
The amount of each instalment be \[Rs.\ 360\]
Option A). \[Rs.\ 360\]

Note: Simple interest is calculated by multiplying the daily interest rate with the principal by the number of days that elapse between payments. With the use of simple interest, we can calculate the interest without any error by saving time and effort .