Question

Rounaq took a loan from Ramesh at a rate of 10% per annum for 5 years. At the end of 5 years, he paid the total amount as Rs. 90,000. What was the amount he took as a loan?

(a) Rs. 1,00,000
(b) Rs. 90,000
(c) Rs. 60,000
(d) Rs. 80,000

Answer 1

Rounaq took a loan which, after applying a simple interest formula, shows that the original amount borrowed was Rs 60,000. This was calculated by dividing the total amount paid after 5 years by the sum of 1 plus the product of the interest rate and time.

Step-by-step explanation:

To find out the loan amount that Rounaq took from Ramesh, we need to use the formula for simple interest and the total repayment amount that includes both the principal and the interest earned over the course of 5 years. In this particular problem, the simple interest formula is:

Interest = Principal × Rate × Time

Let's denote the principal, which is the original loan amount, as P, the rate as r (expressed as a decimal), and the time as t years; knowing that the rate is 10% (or 0.10 when expressed as a decimal) and the time is 5 years, we get:

Interest = P × 0.10 × 5

The total amount paid after 5 years, which is the sum of the principal and the interest, is Rs 90,000. We know that:

Total Amount = Principal + Interest

Rs 90,000 = P + (P × 0.10 × 5)

By solving for P, we will find the original loan amount.

Rs 90,000 = P + (0.5 × P)

Rs 90,000 = 1.5P

Now, divide both sides by 1.5 to isolate P:

P = Rs 90,000 / 1.5

P = Rs 60,000

Therefore, the amount Rounaq took as a loan was Rs 60,000.