Question

Find the simple interest and the amount of Rs.2400 for 3 years 5 months and 15 days at the rate of 9%.

Answer 1

Hint: In this question, we need to determine the simple interest as well as the amount accumulated on Rs.2400 after 3 years 5 months and 15 days at the rate of 9%. For this, we will use the relation between the simple interest, principle amount, time period and the rate of interest.

Complete step-by-step answer:
The product of the principal amount, time period and the decimal equivalent of the rate of interest results in the simple interest gained on the principal amount. Mathematically, $ SI = prt $ where ‘p’ is the principal amount, ‘r’ is the decimal equivalent of the rate of interest and ‘t’ is the time period for which the interest is gained (in years).
According to the question, the time period for which the simple interest need to be calculated is 3 years 5 months and 15 days which should be converted into years. So,
\[
\Rightarrow 3{\text{ }}years{\text{ }}5{\text{ }}months{\text{ }}and{\text{ }}15{\text{ }}days = 3 + \dfrac{5}{{12}} + \dfrac{{15}}{{365}} \\
   = 3 + 0.4166 + 0.0410 \\
   = 3.457{\text{ years}} \\
 \]
So, we need to calculate the simple interest for the sum of Rs.2400 for 3.457 years at the rate of 9%.
\[
\Rightarrow SI = prt \\
   = 2400 \times \dfrac{9}{{100}} \times 3.457 \\
   = 746.712 \\
 \]
Hence, the simple interest gained on the amount Rs.2400 at 9% interest rate in the time period of 3 years 5 months and 15 days is Rs.746.712.
The summation of the principal amount and the simple interest results in the total amount accumulated in the given time period. Mathematically, $ A = p + SI $ .
So, substituting the value of p as 2400 and the simple interest as 746.712 in the equation $ A = p + SI $ to determine the amount.
 $
\Rightarrow A = p + SI \\
   = 2400 + 746.712 \\
   = 3146.712 \\
  $
Hence, the amount accumulated is Rs.3146.712 and the simple interest is Rs.746.712.

Note: Students must convert the time period in the units of years before substituting it in the desired equation. Moreover, amount is the total sum of money that the investor will get in return as the result of investing a sum of money (principle amount) for the specified period of time at specified interest rate.