Question

Karthik sold a property and deposited half of the money he received in a bank where the interest is calculated as simple interest. he deposited the remaining amount in another bank with interest compounded annually. the difference between the compound interest and simple interest he received for 2 years at 8% interest is ₹ 800. find the amount karthik got by selling the property.

Answer 1

To find the total amount Karthik received from the property sale, we calculated the simple and compound interests on half of the total amount and used the given interest difference to determine the total amount, which is ₹250,000.

Step-by-step explanation:

The student's question is about finding the total amount Karthik received from selling a property, given that he deposited half the amount in a bank with simple interest and the other half with compound interest, and the difference between the two interests over 2 years at 8% rate is ₹800. To solve this, we need to use the formulas for computing simple and compound interest. Let's assume the total amount Karthik received for the property is 2P. This means he deposited P in each bank. The simple interest on P after 2 years at an 8% rate would be calculated using the formula SI = (P × R × T) / 100, where R is the rate and T is the period in years. In this case, SI = (P × 8 × 2) / 100 = 0.16P.

For the compound interest, the formula is CI = P × [(1 + R/100)^T - 1]. Therefore, the compound interest after 2 years at an 8% rate is CI = P × [(1 + 8/100)^2 - 1] = P × [(1.08)^2 - 1] = P × (1.1664 - 1) = 0.1664P. The difference between compound interest and simple interest is given as ₹800. So, 0.1664P - 0.16P = 800 = 0.0064P. Solving for P gives us P = 800 / 0.0064 = 125000. Therefore, the total amount Karthik received by selling the property is 2P = 2 × 125000 = ₹250000.