Question

Anita takes a loan of Rs. 5000 at 15% per year as rate of interest. Find the amount she has to pay at the end of 2 years.

Answer 1

Hint: First calculate simple interest (SI) by using the relation $\dfrac{\text{P }\!\!\times\!\!\text{ R }\!\!\times\!\!\text{ T}}{\text{100}}\text{= SI}$, where P is the amount (principal) at which rate of interest R (in percentage) will take place for time period of T years. Use relation for calculating total amount after T years given as:
Compound money = S.I. + principal amount.

Complete step-by-step answer:

As we know that simple interest at any amount ‘P’ with interest R% for duration of ‘T’ time period is given by relation
$S.I=\dfrac{\text{P }\!\!\times\!\!\text{ R }\!\!\times\!\!\text{ T}}{\text{100}}$ ……….. (i)

Where T is in years and R is in % .

Now, it is given in the problem that Anita is taking a loan of 5000 Rs at 15% per year and hence, we need to determine the amount she has to pay at the end of the 2 years.

So, we can calculate the amount of interest with the amount of interest with the relation given in the equation (i), where we can put P = 5000 Rs, r = 15 and T = 2 years.

Hence, on substituting the values of P, R, T from the problem to the equation, we get
$\begin{align}
  & SI=\dfrac{5000\times 15\times 2}{100} \\
 & \Rightarrow SI=50\times 15\times 2=Rs.1500 \\
\end{align}$

Hence, Anita has to pay Rs.1500 as an interest.

As we know that the total amount after ‘T’ years with principal amount P can be given by sum of principal amount and interest of R per year at the principal amount.
Hence, we get total amount after interest = principal amount + simple interest.

Hence, Anita has to pay the principal amount of the loan and interest on this amount as well. As we have already calculated the simple interest on the given amount with the given conditions in the problem.

Hence, Anita has to pay Rs.5000 of loan and Rs.1500 of simple interest both after 2 years.

So, she has to pay 5000 + 1500 =Rs. 6500 after 2 years.

Note: Don’t confuse the formula of simple interest and compound interest. We apply C.I. formula where the principle amount increases with a fraction rate. And both terms will be mentioned in the question as well. So, be clear with the terminologies and don’t go wrong with it.
One may forget to add the principal amount with the simple interest calculated, as the total amount paid for loan should be higher than it and given as sum of principal amount and interest on it. Hence, be clear with it as well and don’t forget to add both the amounts.