Question

Find the amount to be paid at the end of 3 years in case principal is Rs. 1200 at 12% per annum.

Answer 1

Hint: We will assume the amount to be A and then we will substitute all the values given in formula of simple interest \[\text{S}\text{.I=}\dfrac{\text{P }\!\!\times\!\!\text{ R }\!\!\times\!\!\text{ T}}{\text{100}}\] and we will substitute \[\text{A=P+S}\text{.I}\] in this formula and hence we will calculate the principal.

Complete step-by-step answer:
Before proceeding with the question we should understand the concept of principal, amount and simple interest rate.
Simple Interest (S.I) is the method of calculating the interest amount for some principal amount of money.
The Formula for simple interest helps us to find the interest amount if the principal amount, rate of interest and time periods are given. Simple interest formula is given as \[\text{S}\text{.I=}\dfrac{\text{P }\!\!\times\!\!\text{ R }\!\!\times\!\!\text{ T}}{\text{100}}.......\text{(1)}\] where SI is simple interest, P is principal, R is interest rate, T is time period.
In order to calculate the total amount, the following formula is used \[\text{A=P+S}\text{.I}.....\text{(2)}\] where A is the amount and P is the principal. Amount(A) is the total money paid back at the end of the time period for which it was borrowed.
Rate of interest(R) given is 12% and principal is Rs. 1200. Also the time period(T) is 3 years. So let the amount be A. Using this information and substituting all the values in equation (1) we get the simple interest as,
\[\text{S}\text{.I=}\dfrac{\text{1200 }\!\!\times\!\!\text{ 12 }\!\!\times\!\!\text{ 3}}{\text{100}}.......\text{(3)}\]
Solving equation (3) by cancelling similar terms and then multiplying the rest we get,
\[\text{S}\text{.I=12}\times \text{12}\times \text{3=432}.....\text{(4)}\]
Now substituting the value of S.I from equation (4) and the principal of Rs. 1200 in equation (2) we get,
\[\text{A=1200+432=1632}\]
Hence the amount is Rs. 1632.

Note: Remembering the formula of simple interest and amount is the key here. We in a hurry may commit a mistake in solving equation (3) so we need to be careful with the basic calculation steps. We just have to put the values in the formulas and we will get the answer.