A scheme offers compound interest at the rate of 5% pa, compounded half-yearly. If a man invests ₹ 14000 each on 1st January and 1st July, what will be the total interest earned by him at the end of the year?₹ 2135₹ 1058.75₹ 1835.75₹ 1478.50

To solve this problem, we need to understand that the interest is compounded semi-annually, which means it is calculated twice a year.

Step 1: Calculate the interest for the first investment of ₹ 14000.

The formula for compound interest is A = P (1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

In this case, P = ₹ 14000, r = 5/100 = 0.05 (converted to decimal), n = 2 (since it is compounded semi-annually), and t = 1 year.

So, A = 14000 * (1 + 0.05/2)^(2*1) = ₹ 14735.

The interest earned for the first investment is A - P = ₹ 14735 - ₹ 14000 = ₹ 735.

Step 2: Calculate the interest for the second investment of ₹ 14000.

Since the second investment is made in July, it is only invested for half a year. So, t = 0.5 year.

So, A = 14000 * (1 + 0.05/2)^(2*0.5) = ₹ 14200.75.

The interest earned for the second investment is A - P = ₹ 14200.75 - ₹ 14000 = ₹ 200.75.

Step 3: Add the interest earned from both investments.

Total interest = ₹ 735 + ₹ 200.75 = ₹ 935.75.

So, the total interest earned by the man at the end of the year is ₹ 935.75. This option is not listed in the given choices, so there might be a mistake in the question or the provided options.