Question

If a certain principal amounts to 55000 at 15% per annum over 4 years, how much will be the amount in 6 years in rupees? (considering simple interest)

Answer 1

Hint: We will assume the principal to be x 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 \[\text{S}\text{.I=A-P}\] 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 you 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 and 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 15% and amount(A) is Rs. 55000. Also the time period(T) is 4 years. So let the principal be x. Using this information and substituting all the values in equation (1) and equation (2), we get,
\[\text{S}\text{.I=}\dfrac{x\text{ }\!\!\times\!\!\text{ 15 }\!\!\times\!\!\text{ 4}}{\text{100}}.......\text{(3)}\] and \[55000-x\text{=S}\text{.I}.....\text{(4)}\]
Now from equation (4) substituting the value of S.I in equation (3) we get,
\[55000-x\text{=}\dfrac{x\text{ }\!\!\times\!\!\text{ 15 }\!\!\times\!\!\text{ 4}}{\text{100}}.......\text{(5)}\]
Rearranging and solving for x we get,
\[\begin{align}
  & \Rightarrow 100(55000-x)=60x \\
 & \Rightarrow 5500000=100x+60x \\
 & \Rightarrow 160x=5500000 \\
 & \Rightarrow x=\dfrac{5500000}{160}=34375.......(6) \\
\end{align}\]
Now we have calculated the principal as Rs. 34375. The new time period(T) is 6 years and the rate of interest(R) is the same as 15%. So using this information we calculate simple interest.
\[\text{S}\text{.I=}\dfrac{\text{34375 }\!\!\times\!\!\text{ 15 }\!\!\times\!\!\text{ 6}}{\text{100}}=30937.5.........(7)\]
Substituting the value of S.I and principal in equation (2) we get,
\[\text{A=34375+30937}\text{.5=65312}\text{.5}\]
Hence the principal amounts to Rs. 65312.5 in 6 years.

Note: Remembering the formula of simple interest and amount is the key here. We in a hurry may commit a mistake in solving for x in equation (5) so we need to be careful with the basic calculation steps. Also we can take the rate of interest something else so we need to verify again by reading the question properly.