Question

A certain sum invested at 4% per annum compounded semi-annually amounts to Rs. 1,20,000 at the end of one year. Find the sum.

A. Rs. 116,000
B. Rs. 114,000
C. Rs. 112,000
D. Rs. 110,000

Answer 1

To find the principal amount, use the formula for compound interest. Substituting the given values, the principal amount is Rs. 112,000.

Step-by-step explanation:

To find the principal amount, we can use the formula for compound interest:

P = A / (1 + r/n)^(nt)

Where:

• P = principal amount
• A = final amount
• r = annual interest rate (as a decimal)
• n = number of times interest is compounded per year
• t = time in years

In this case, the final amount is Rs. 1,20,000, the interest rate is 4% (0.04 as a decimal), the interest is compounded semi-annually (n = 2), and the time is 1 year. Substituting these values into the formula:

P = 120000 / (1 + 0.04/2)^(2*1)

P = 112000

Therefore, the principal amount is Rs. 112,000. So the correct answer is C. Rs. 112,000.