In day-to-day life dealings, simple interest is seldom calculated. The interest which the banks, Insurance corporations and other money lending and deposit- taking agencies calculate is not the simple interest, but the compound interest. To understand what compound interest is, let us take an example:
A man deposits $5000 in a finance company at 10% per annum. What interest does he get in One year? At end of one year if he decides to deposit the whole sum(amount after 1 year) for another year, what interest does he get at the end of (a) the second year (b) in two years?
\(\textrm{Interest for the first year} =\frac{ 5000 \times 1 \times 10} {100} = 500\)
Amount after one year = $5000+ $500 = $5500
When $5500 is again deposited in the company for one year, it becomes the principal for the second year.
\(\textrm{Interest for the second year} =\frac{ 5500 \times 1 \times 10} {100} = 550\)
Thus interest for two year is $500 + $ 550 = $1050
Notice that the interest for the second year is more than the first year. Because for the second year interest on interest is calculated. Interest calculated in this manner is known as Compound Interest(C.I).
When Interest at the end of each fixed period is added to the principal and the amount thus obtained is taken as the principal for the next period, the interest calculated in this way is the compound Interest.
So what is the difference between Simple Interest and Compound Interest?
Simple interest(S.I) is paid on the principal only whereas Compound interest is paid on the sum of the original principal and accumulated past interest. For the first year simple interest and compound interest will be the same and from the second year onwards the compound interest is more than the simple interest.
Formula:
P invested at r% per annum compound interest for n years will become an amount A, then
\(A = P( 1 + \frac{r}{100})^n\)
Compound Interest = A − P
Note: If the rate of interest is different for every year, say r1, r2 and r3 for the first, second and third year. Then Amount A after 3 years is
\(A = P( 1 + \frac{r_1}{100})( 1 + \frac{r_2}{100})( 1 + \frac{r_3}{100})\)
