Question

Payal took a loan of $Rs.12,000$ for parlour from a nationalized bank. How much amount she will repay after $2$ years $6$ months at an annual rate of $8\% $. When interest is accumulated annually.

Answer 1

Hint: Whenever we have this type of problem, in order to find the amount to be paid after $2$ years $6$ months. First convert the months to year so that the simplification becomes easier. Then we need to find the interest by using the formula given by: $I = \dfrac{{P \times t \times r}}{{100}}$ and then by adding the interest amount with the principal amount we get the required answer.

Complete Step by Step Solution:
Here in this question they have given the principal amount, rate of interest per year and the time period and asked us to find the actual amount he has to pay after $2$ years $6$ months. Whenever we need to solve problems the value should be in one unit so the time period here given is $2$ years $6$ months so now first convert $6$ months to years and then add with the $2$ years to get the total time period in years. As we know there are $12$ months in a year, now divide the $6$ months by $12$ to get the value in terms of years.
Therefore we get $6months = \dfrac{6}{{12}} = 0.5years$. Hence the total time period is $2 + 0.5 = 2.5$ years.
To solve this problem first we need to find the interest amount by using the formula given by:
$I = \dfrac{{P \times t \times r}}{{100}}$
Where, $P$ is principal amount which is $Rs.12,000$
              $t$ is time period which is $2.5$ years and
             $r$ is the rate of interest which is $8\% $ .
Now substitute all these values in the above given formula to find the interest amount.
Therefore, we get
$I = \dfrac{{12,000 \times 2.5 \times 8}}{{100}}$
$ \Rightarrow I = \dfrac{{240,000}}{{100}}$
$ \Rightarrow I = 2,400Rs$
Now, we have the interest amount for $2.5$ years that is $Rs.2,400$ and also we know the principal amount which is $Rs.12,000$ . In order to find the actual amount Payal has to pay is by using the below formula.
$A = P + I$
Where, $A$ is actual amount to be paid after $2.5$ years
              $P$ is principal amount which is $Rs.12,000$ and
              $I$ is interest amount for $2.5$ years which is $Rs.2,400$
Now, by substituting these values in the actual amount formula we get
$A = 12,000 + 2,400$
$A = 14,400Rs$

Therefore, Payal has to pay $Rs.14,400$ after $2.5$ years.

Note:
Whenever we have this type of problem, first convert the time period in terms of years. If we know the formula to find the interest amount and the actual amount formula then it’s enough to get the correct answer. Sometimes they may give rate of interest per half year, or for quarter year also. In that case you need to take the interest accordingly.