Question

Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in scheme B ?
1) Rs 6400
2) Rs 6500
3) Rs 7200
4) Rs 7500

Answer 1

Hint: The above problem is based on the simple interest concept.
Simple interest is the interest calculated on the principal and not on the interest on interest.
Formula for simple interest is given by:
$SI = \dfrac{{P \times R \times T}}{{100}}$ (SI is the interest, P is the principal, R is the rate and T is the time)
Using the formula of simple interest we will solve the given problem.

Complete step-by-step solution:
Let's explain the Simple interest in more detail and then we will solve the given problem.
Simple interest is the interest calculated on the principal portion of a loan or the original contribution to a savings account. Simple interest does not compound, meaning that an account holder will only gain interest on the Principal and the borrower will never have to pay interest on interest already accrued.
Now, we will do the calculation part of the problem;
We have the total investment Rs 13,500
Therefore, Let the scheme A had invested sum P and scheme B invested sum 13500-P.
Simple interest for scheme A is;
$ \Rightarrow SI = \dfrac{{P \times 14 \times 2}}{{100}}$ (Interest rate for 14% and time is 2 yrs)........................1
Simple interest for scheme B be ;
$ \Rightarrow SI = \dfrac{{\left( {13900 - P} \right) \times R \times T}}{{100}}$ .....................2 (rate of interest is 11% for 2 years)
Total simple interest given to us in the question is Rs 3508
Thus, We will add the interest of scheme A and scheme B and equate it to the total interest.
$ \Rightarrow 3508 = \dfrac{{P \times 14 \times 2}}{{100}} + \dfrac{{(13900 - P) \times 11 \times 2}}{{100}}$ (On solving further)
$ \Rightarrow 350800 = 28P + \left( {13900 - P} \right)22$ (Rearranging the terms)
$ \Rightarrow 350800 - 308500 = 28P - 22P$
$ \Rightarrow 45000 = 6P$
$ \Rightarrow P = 7500Rs$
Principal amount is $7500$ Rs scheme A has invested.
Principal amount of scheme B is;
$13900 - 7500 = 6400$ Rs

Option 1 is the correct answer.

Note: Although compound interest is calculated generally and mostly used by the borrowers but there are many other applications such as Bonds use non compounding interest, mortgages are mostly based on compound interest but there are interests which are non compounding and various effective annual interest.