Question

What will be the total amount (Principal amount +Interest) of Rs.750 as principal at the rate of 8% for $4\dfrac{1}{2}$ years?
A. Rs.1020
B. Rs.1030
C. Rs.1040
D. Rs.1050

Answer 1

Hint: In order to solve this problem we need to solve the mixed fraction first to get the total amount of duration for the money to be calculated and then we will get the total amount interest by multiplying the interest of one year with the total duration and then calculate the percentage of interest imposed till the end of the durations after that we will add the actual amount with the increased amount to get the answer.

Complete step by step answer:
The actual amount whose interest to be calculated is Rs.750
We know that $4\dfrac{1}{2}$ years means $\dfrac{{4 \times 2 + 1}}{2} = \dfrac{9}{2}$ = 4.5 years.
Interest imposed on Rs.750 per year is 8%.
Then the interest imposed on amount on 4.5 years is 8 x 4.5 = 36%
So, the interest increased in 4.5 years is $750 \times \dfrac{{36}}{{100}} = 270$.
So, the interest is Rs.270 and the principal amount is Rs.750 we need to find the total amount that is principal amount + interest to get the right answer.
So, principal amount + interest = 750 + 270 = Rs.1020

So, the correct answer is “Option A”.

Note: Whenever you get such problems to solve you need to know that the mixed fraction $a\dfrac{b}{c}$ can be written as $\dfrac{{ab + c}}{b}$ and the principal amount is the first amount which is provided to calculate the interest. There are various such types of problems which include various different conditions like here it has included the mixed fraction, we can also deal with profit-loss in place of mixed fraction or any other concept nut ultimately we have to calculate the interest and get the required answer. We can also solve this problem using the formula of simple interest that is the final amount is equal to principal amount(1+(interest rate )(time)) Taking care of such things will give you the right answer.