Question

Find the time when simple interest on Rs.3.3 Lakhs at 6.5 % per annum is Rs. 75075.

Answer 1

Hint: In this question, the principal amount, rate per annum, and Simple Interest are given. We have to substitute the values of simple interest, principal amount, and rate of interest per annum in the formula of simple interest,
\[S.I=\dfrac{P\times r\times t}{100}\]

Complete step-by-step solution:
Simple interest can be determined by multiplying the interest rate per annum by the principal by the number of years
Here, we have the principal amount, P = Rupees 3,30,000, the rate, r = 6.5 % per annum and the simple interest, S.I = Rupees 75,075.
Let us find the time when the S.I, Principal amount, and the rate per annum is given.
We know,
The Formula to calculate Simple Interest is,
\[S.I=\dfrac{P\times r\times t}{100}\]
Substituting the values of Principal amount, the rate per annum, and time in the above-given formula, we get the following equation.
\[75075=\dfrac{330000\times 6.5\times t}{100}\]
Now, multiply by 100 on both the sides of the equation, we get
\[75075\,\times 100=\dfrac{330000\times 6.5\times t}{100}\times 100\]
Also divide by 330000 x 6.5 on both the sides of the equation, we get
\[t=\dfrac{75075\times 100}{330000\times 6.5}\]
After, further calculations we will get the time taken.
\[t=3.5\] years.

Note: Simple interest is the easiest method of calculating the interest charged on a loan. The rate of interest also has units in the form of p.c.p.a. The formula which has been used, instead of ‘t’ we can also use ‘N’ which is basically the number of years. Always, check your solution to see if we have to input the correct units to the required values. To find the final amount relative to the principal, rate of interest, and time taken, A = P(1+rt).