Find the compound interest on ₹12800 for 1 year at 15/2% per annum compounded semi annually.
12800((1+.15/4)^2 - 1)
1992
Amount=14792 and compound interest=1992
To find the compound interest, we need to use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including principal and interest)
P = the principal amount (₹12,800 in this case)
r = the rate of interest per annum (15/2% or 0.075 as a decimal)
n = the number of times the interest is compounded per year (semi-annually, so it's 2)
t = the time period in years (1 year in this case)
Plugging in the values, we get:
A = 12800(1 + 0.075/2)^(2*1)
Now, let's solve this equation step by step:
Step 1: Calculate the value inside the brackets:
1 + 0.075/2 = 1.0375
Step 2: Raise this value to the power of 2:
(1.0375)^(2) = 1.076890625
Step 3: Multiply the principal amount (₹12,800) by the value obtained in Step 2:
A = 12800 * 1.076890625
Step 4: Calculate the compound interest by subtracting the principal amount (₹12,800) from the final amount (A):
Compound interest = A - P = (12800 * 1.076890625) - 12800
Calculating this, we find:
Compound interest = ₹779.425
Therefore, the compound interest on ₹12,800 for 1 year at 15/2% per annum compounded semiannually is ₹779.425.