COMPOUND INTEREST

                 COMPOUND INTEREST

What Is Compound Interest?

Compound interest (or compounding interest) is interest calculated on the initial principal, which also includes all of 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. 

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Solution:
Let P = 20000, r = 6%, n = 3
using formula
A=P(1+r)n=20000(1+.06)3=23820.32$\text{A}=\text{P}{\left(1+\text{r}\right)}^n=20000{\left(1+.06\right)}^3=23820.32$

The compound interest =23820.32−20000=3820.32$=23820.32-20000=3820.32$

Example 02:
Find the compound amount which would be obtained from the interest of Rs.2000 at 6% compounded quarterly for 5 years.

Solution:
Let principal = 2000, r=6%=64×100=.015$r=6\mathrm{\%}=\frac{6}{4\times 100}=.015$, n=5×4=20quarters$n=5\times 4=20\text{quarters}$

∴A=P(1+r)n=2000(1+.015)20=2693.71$$\therefore A=P{\left(1+\text{r}\right)}^n=2000{\left(1+.015\right)}^{20}=2693.71$$

Example 03:
Find compound interest on Rs.2500 invested at 6% per annually, compound semi-annually for 8 years.

Solution:
Let Principal = 2500, r=6%=0.06616=0.03$r=6\mathrm{\%}=0.06\frac{6}{16}=0.03$, n=8×2=16$n=8\times 2=16$
We know that
A=P(1+r)n=2500(1+.03)16=4011.73