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

FUTURE VALUE

            PRESENT AND FUTURE VALUE

What is Future Value (FV)?

Future value (FV) is the value of a current at a specified date in the future based on an assumed rate of growth.

If, based on a guaranteed growth rate, a $10,000 investment made today will be worth $100,000 in 20 years, then the FV of the $10,000 investment is $100,000. The FV equation assumes a constant rate of growth and a single upfront payment left untouched for the duration of the investment.

FORMULA OF FUTURE VALUE

FV=I×(1+(R×T))where:I=Investment AmountR=Interest RateT=Number of yearsFuture value with simple interest is calculated in the following manner:


Future Value = Present Value x [1 + (Interest Rate x Number of Years)]

For example, Bob invests $1,000 for five years with an interest rate of 10%. The future value would be $1,500.

Future Value = $1,000 x [1 + (0.1 x 5)]
Future Value = $1,000 x 1.5
Future Value = $1,500

Future value with compounded interest is calculated in the following manner:

Future Value = Present Value x [(1 + Interest Rate) ^{Number of Years}]

For example, John invests $1,000 for five years with an interest rate of 10%, compounded annually. The future value of John's investment would be $1,610.51.

Future Value = $1,000 x [(1 + 0.1)⁵]
Future Value = $1,000 x 1.61051
Future Value = $1,610.51


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