Find the Compound Interest on a sum of Rs.1000 at the rate of 10% per annum for 1.5 years wheninterest is compounded half-yearly

Sure, here is the step by step solution:

Step 1: Identify the given values Principal (P) = Rs. 1000 Rate of interest (r) = 10% per annum Time (t) = 1.5 years Since the interest is compounded half-yearly, we need to adjust the rate and time accordingly.

Step 2: Adjust the rate and time for half-yearly compounding The rate becomes half, i.e., r = 10/2 = 5% per half-year The time becomes double, i.e., t = 1.5*2 = 3 half-years

Step 3: Substitute the values in the formula for compound interest The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount after time t, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per time period, and t is the time. Here, n = 2 (since interest is compounded half-yearly), so the formula becomes A = P(1 + r/2)^(2t)

Step 4: Calculate the amount (A) A = 1000(1 + 5/100)^6 = 1000(1.05)^6 = Rs. 1340.10

Step 5: Calculate the compound interest The compound interest is given by the formula CI = A - P CI = 1340.10 - 1000 = Rs. 340.10

So, the compound interest on a sum of Rs.1000 at the rate of 10% per annum for 1.5 years when interest is compounded half-yearly is Rs. 340.10.