Simple and Compound Interest

Simple interest

Simple interest charges the same fee every period, always calculated on the original principal $P$ :

SI = \dfrac{P \times N \times R}{100}

where $N$ is the number of years and $R$ the annual rate as a percentage.

Worked example: Find the simple interest on $\text{₹}25{,}000$ borrowed for 3 years at 9% per annum.

SI = \dfrac{25000 \times 3 \times 9}{100} = 6750

The total amount repaid is $A = P + SI = 25000 + 6750 = 31{,}750$ .

Compound interest: interest on interest

Compound interest adds each period's interest back into the principal before computing the next period's interest, so later interest is earned on more than just the original sum. Using the same numbers as above, $\text{₹}25{,}000$ at 9% annually, compounded once a year:

I_1 = 25000 \times \dfrac{9}{100} = 2250 \quad\Rightarrow\quad \text{new principal} = 27{,}250

I_2 = 27250 \times \dfrac{9}{100} = 2452.5 \quad\Rightarrow\quad \text{new principal} = 29{,}702.5

I_3 = 29702.5 \times \dfrac{9}{100} = 2673.225

Total interest over 3 years: $2250 + 2452.5 + 2673.225 = 7375.725$ , more than the $\text{₹}6750$ simple interest gave, even though the principal and rate are identical.

The same result comes directly from the compound interest formula, with $n$ compounding periods per year over $t$ years:

CI = P\left(1+\dfrac{r}{100n}\right)^{nt} - P

With annual compounding ( $n=1$ ):

CI = 25000(1.09)^3 - 25000 = 25000(1.295029) - 25000 = 7375.725