Question

If Rs.62500 for 2 years 6 months at 12% per annum compounded annually. Find the amount.

Answer 1

Hint: Here we can calculate the compounded annually by dividing time into multiple parts for easy calculations. Once time is divided into partitions of 1 year or less, we will just have to find simple interest and update the principle amount accordingly for new calculations.
Formula used: Simple Interest =\[\dfrac{{P*R*T}}{{100}}\], Amount = Principle + Simple Interest.

Complete step-by-step answer:
Important points given in the question:
1. Principle = 62500 Rs.
2. Time =2 Years 6 months = 2.5 Years
3. Rate of Interest =12%
Let T=time, P=principle , R= rate of interest. So, we can access them easily.
Let’s start by calculating the simple interest.
Simple Interest = \[\dfrac{{P*R*T}}{{100}}\]
Substituting values of P, R, and T.
\[ \Rightarrow \dfrac{{62500*1*12}}{{100}}\]
Multiplying all the numerator values to simplify it.
\[ \Rightarrow \dfrac{{{\rm{750000}}}}{{100}}\]
Cancelling zeros.
We get Simple Interest = \[7500Rs\] .
Now, we will calculate the amount of the 1st year.
Amount = Principal + Interest.
Amount = \[62500 + 7500 \Rightarrow Rs.70000\]
Now New Principle will be = \[Rs.70000\]
Again applying the formula to calculate simple interest with new principle,
Simple Interest = \[\dfrac{{P*R*T}}{{100}} \Rightarrow \dfrac{{70000*12*1}}{{100}} \Rightarrow 8400Rs.\]
Now, we will calculate the amount of the 2nd year.
Amount = Principal + Interest.
Amount = \[70000 + 8400 = Rs.78400\]
Now this will be the New Principle = \[Rs.78400\]
Again applying the formula to calculate simple interest with new principle,
As we are finding for the next half year. So time will be 0.5 years.
Simple Interest = \[\dfrac{{P*R*T}}{{100}} \Rightarrow \dfrac{{78400*12*0.5}}{{100}} \Rightarrow 4704Rs.\]
So, Final Amount that is compounded annually,
Amount = Principle + Simple Interest
= \[78400{\rm{ }} + {\rm{ }}4704\]
 = \[Rs.83104\]


Note: In these types of questions you are given with P, R, T and you have to calculate simple interest and amount or 1 year each. Then, while calculating the amount for the last year will be the compound annually. Do not forget to update the principal while calculating the simple interest.