Question

A borrows 5000 at simple interest. At the end of 3 years, he again borrows 3000 and finally pays 2340 as interest after 6 years. From the time he had made the first borrowing. Find the rate of interest.

Answer 1

Hint: We know that A takes two loans. First loan is with principal amount 5000 with time as 6 years. Second loan is with principal amount 3000 for a time of 3 years. Now we know that simple interest is given by P × r × t. where P is principal amount, r is rate of interest and t is time for which money is borrowed. Now we have the sum of both interests is 2340 hence we can easily find out r.

Complete step by step answer:
Now A borrows a loan of 5000 at simple interest.
Let us say the rate of interest is r percent.
Now let us calculate the interest on the amount 5000 after 6 years.
We know that simple interest is given by P × r × t. where P is principal amount, r is rate of interest and t is time for which money is borrowed.
Hence we get
Interest = 5000 × r × 6
Interest = 30,000 × r.
Let us call this interest as ${{I}_{1}}$
Hence we have ${{I}_{1}}=30000\times r......................\left( 1 \right)$
Now we are given A takes a loan again after 3 years.
Now he pays the interest after total 6 years from first loan
Hence the time for which the second loan is borrowed is 3 years.
Now we have principal amount of this loan is 3000
Hence again using the formula interest = P × r × t we get.
Interest = 3000 × r × 3
Interest = 9000 × r.
Let us say this interest as ${{I}_{2}}$
Hence we have ${{I}_{2}}=9000\times r......................\left( 2 \right)$
Now we are given that the total interest is 2340.
Hence we have ${{I}_{1}}+{{I}_{2}}=2340$
Now from equation (1) and equation (2) we get
$\begin{align}
  & 30000\times r+9000\times r=2340 \\
 & \Rightarrow 39000\times r=2340 \\
 & \Rightarrow r=\dfrac{2340}{39000}=\dfrac{6}{100} \\
\end{align}$

Hence the interest rate is 6 percent per annum.

Note: Note that in the formula SI = P × r × t we have r in percent. Hence when we calculate r we keep it with denominator 100 so as to calculate the percentage. Also note that simple interest is given by (P × r × t) while compound interest compounded annually is given by $P{{\left( 1+r \right)}^{t}}$ . Do not get confused between both formulas as they have the same variables.