Compound Interest
Compound interest (or compounding interest) is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Thought to have originated in 17th-century Italy, compound interest can be thought of as “interest on interest,” and will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount. The rate at which compound interest accrues depends on the frequency of compounding; the higher the number of compounding periods, the greater the compound interest. Thus, the amount of compound interest accrued on $100 compounded at 10% annually will be lower than that on $100 compounded at 5% semi-annually over the same time period.
Formulae used
P = Principal
R = Rate % per annum,
n= Time in years.
When interest is compound Annually:
\[Amount = p\left ( 1 + \frac{R}{100} \right )^{n} \]
When interest is compounded Half-yearly:
\[Amount = p\left ( 1 + \frac{R/2}{100} \right )^{2n} \]
When interest is compounded Quarterly:
\[Amount = p\left ( 1 + \frac{R/4}{100} \right )^{4n} \]
