Interest compounded annually (or) Half Yearly (Semi Annually)

Compound Interest with Different Compounding Periods

Compound Interest varies based on how frequently interest is compounded. Let's understand with a new example:

Calculate the compound interest on Rs. 2000 for 2 years at 12 % per annum when interest is compounded:

(a) Annually (b) Semi-annually (half-yearly)

Formula: A = P1+R100n

Where: A = Final Amount P = Principal R = Interest Rate per period n = Number of periods

(a) Annually: R = 12 %, n = 2

Substituting:

A = 20001+121002 = 20001.122 = Rs. (Upto two decimal places)

CI = Rs. - Rs. = Rs. (Upto two decimal places)

(b) Semi-annually: R = % (12% ÷ 2) , n = (2×2)

A = 20001+61004 = 20001.064 = Rs. (Upto two decimal places)

CI = Rs. - Rs. = Rs. (Upto two decimal places)

Thus,

When compounded semi-annually:

Semi-annual compounding yields slightly higher returns than annual compounding.

The shorter the conversion period, the higher the final amount.

Chapter 5: Comparing Quantities using Proportion