Question

For higher education, Trusha borrows Rs. 9600 from the post-office for \[2\dfrac{1}{2}\] years at the rate of 9%. How much interest and amount would she pay back at the end of the term?
(A) Interest = Rs. 1050, Amount = Rs. 10,650
(B) Interest = Rs. 2160, Amount = Rs. 11,760
(C) Interest = Rs. 1050, Amount = Rs. 12,360
(D) Interest = Rs. 1050, Amount = Rs. 10,650

Answer 1

Hint: The principal, time, and rate of interest are Rs. 9600, 2.5 years, and 9% respectively. We know the formula, Simple interest = \[\dfrac{\text{Principal}\times \text{Rate}\times \text{Time}}{100}\] . Use this formula and get the value of the simple interest. Now, use the formula, \[\text{Amount=Principal+Simple}\,\text{interest}\] and get the value of the amount.

Complete step-by-step answer:
According to the question, it is given that Trusha borrows Rs. 9600 from the post-office for \[2\dfrac{1}{2}\] years at the rate of 9%. We have to find the amount that she would pay back at the end of the term.
The principal borrowed from the post-office = Rs. 9600 ………………………………..(1)
The duration of time = \[2\dfrac{1}{2}\] years = 2.5 years ……………………………….(2)
The rate of interest per annum = 9% …………………………………….(3)
We know the formula, Simple interest = \[\dfrac{\text{Principal}\times \text{Rate}\times \text{Time}}{100}\] ………………………….(4)
From equation (1), equation (2), and equation (3), we have the value of the principal, rate of interest per annum, and the time duration.
Now, putting the value of the principal, rate of interest, and the time in the formula shown in equation (4), we get
 Simple interest = \[\dfrac{9600\times 9\times 2.5}{100}=96\times 9\times 2.5=2160\] ……………………………(5)
So, the value of the simple interest on the principal Rs. 9600 for 2.5 years is equal to 2160, Simple interest = Rs. 2160 ……………………..(6)
We know the formula, \[\text{Amount=Principal+Simple}\,\text{interest}\] ……………………….(7)
From equation (1) and equation (6), we have the value of the principal and simple interest respectively.
Simple interest = Rs. 2160 and Principal = Rs. 9600.
Now, putting the value of the principal and simple interest in equation (7), we get
\[\text{Amount=Rs}\text{.9600+Rs}\text{.2160=Rs}\text{.11760}\] …………………………………(8)
The amount is equal to Rs. 11,760.
From equation (6) and equation (8), we have the value of the simple interest and amount.
Therefore, the interest and amount are equal to Rs. 2160 and Rs. 11,760 respectively.
Hence, the correct option is (B).

Note: In this question, one might think to calculate the compound interest and then calculate the amount. But this is wrong because post offices or banks generally follow simple interest rules. So, here we don’t need to calculate the compound interest. Therefore, we need to calculate the simple interest here.