Q.₹20,000 is invested for 1 year at 10% per annum. Find the compound interest if it is compounded

The same nominal rate gives different compound interest depending on how often it is compounded — more frequent compounding gives more interest.

1. Yearly: $A = 20{,}000(1.10)^{1} = 22{,}000$, $CI=₹2{,}000$.
2. Half-yearly: $A = 20{,}000(1.05)^{2} = 22{,}050$, $CI=₹2{,}050$. …

Here $P = ₹20{,}000$, $r = 10\%$ per annum, $t = 1$ year, compared across three compounding frequencies.

1. Compounded yearly ($n=1$):

   $A = 20{,}000\left(1+\frac{10}{100}\right)^{1} = 20{,}000 \times 1.10 = ₹22{,}000, \qquad CI = ₹2{,}000$

2. Compounded half-yearly ($n=2$, periods $=2$, rate/period $=5\%$):

   $A = 20{,}000(1.05)^{2} = 20{,}000 \times 1.1025 = ₹22{,}050, \qquad CI = ₹2{,}050$

3. Compounded quarterly ($n=4$, periods $=4$, rate/period $=2.5\%$): $A = 20{,}000(1.025)^{4} = 20{,}000 \times 1.103812890625 = ₹22{,}076.26, \qquad CI = ₹2{,}076.26$ …

A common misconception is assuming the compound interest should be the same regardless of compounding frequency because the annual rate is the same — this confuses the nominal rate with the a …