Question

If ₹ 600 amount to ₹ 735 in 5 years at a certain rate of simple interest. If the rate of interest is increased by 2%, what will be the amount then?

Answer 1

Hint: In this question, we have been given the amount invested (known as principal), the time for which the principal is invested, the total amount received after the investment period (which includes the principal and the interest). First, we are going to have to calculate the initial rate of interest on the amount invested for 5 years. When we have the calculated rate of interest, we are going to add 2 to it (because it has been given that we need to calculate the amount if the rate of interest is going to be increased by 2% on the initial quantity) and then calculate the amount on the same principal (₹ 600) and the same time for which the investment is made (5 years) and we are going to have our answer.
Formula Used:
We are going to use the formula of simple interest, which is:
\[{\text{interest}} = \dfrac{{principal \times rate \times time}}{{100}}\]

Complete step-by-step answer:
For the initial rate of interest, we have:
Interest,
 \[I = 735 - 600 = 135\]
Principal,
\[P = 600\]
Time,
\[T = 5\]
Rate of interest, \[R = ?\] (to be calculated)
So, applying the formula of simple interest, we have:
\[I = \dfrac{{P \times R \times T}}{{100}}\]
\[135 = \dfrac{{600 \times R \times 5}}{{100}}\]
So we have,
\[R = \dfrac{{135 \times 100}}{{3000}} = 4.5\% \]
Hence, the initial rate of interest is \[4.5\% \] .
Now, when the rate of interest is increased by \[2\% \] , it becomes \[6.5\% \] .
So, \[I = \dfrac{{600 \times 6.5 \times 5}}{{100}} = 195\]
Amount \[ = I + P = 195 + 600 = 795\]
Hence, the amount for this rate of interest is ₹ 795.
So, the correct answer is “₹ 795”.

Note: So, we saw that in solving questions like these, we first write down the things that have been given to us. Then we write down the unknown quantity. Then we think of all the formulae including all the parameters – the known and the unknown. Then we write down the one formula which is the most suitable for all the accounted parameters and is the easiest, with priority always given to the former condition. Then we put in all the values, calculate the result and then we are going to have our answer.