Question

Find the total amount that has to be paid after two years if a principal amount of Rs. 4000 is taken as a loan at a rate of interest of 7.5% per annum? (Assume the interest as simple).

Answer 1

Hint: We start solving the problem by assigning the variables for the required values to find the final amount. We then find the interest that is to be added to the principal amount using the fact that Interest (I) is defined as r% of the principal amount ‘P’ using the formula that x% of y is defined as $\dfrac{x}{100}\times y$. After finding the interest, we add it twice to the principal to find the required amount to be paid after two years.

Complete step by step answer:
According to the problem, we have a principal amount of Rs. 4000 which is to be returned in 2 years with a rate of interest of 7.5% per annum. We need to find the total amount to be returned after two years by adding interest.
Let us assume the principal amount be ‘P’, rate of interest be ‘r’, an interest that is too be added every year as ‘I’ and the amount to be paid after two years as ‘A’.
We know that Interest (I) is defined as r% of the principal amount ‘P’.
So, we have got I = 7.5% of 4000.
We know that x% of y is defined as $\dfrac{x}{100}\times y$.
$\Rightarrow I=\dfrac{7.5}{100}\times 4000$.
$\Rightarrow I=7.5\times 40$.
$\Rightarrow I=300$.
So, the interest of Rs. 300 is to be added to the principal amount every year. Since we need to return the amount in two years, we add Rs. 300 to the principal two times.
So, the final amount (A) to be paid is $Rs.4000+Rs.300+Rs.300=Rs.4600$.
We have found the total amount to be paid after 2 years is Rs. 4600.
∴ The amount that is to be paid after two years is Rs.4600.

Note:
Before solving the problem, we should check whether the interest is simple or compound. If the interest is not simple, we should not proceed as we did in this problem. In compound interest, we calculate interest for the amount that we get after adding interest to the principal after year. Similarly, we can expect problems to find the rate of interest for the given principal amount and the amount that is paid after 2 years.