# Compound Interest

When interest at the end of each conversion period is added to the principal and the amount thus obtained is taken as the principal for the next period, the interest obtained is called Compound Interest.By conversion period, we mean the fixed interval of time at the end of which interest is calculated.

For example, if the interest is compounded semi-annually, then every six months make 1 conversion period. If the interest is compounded monthly, then every month forms a conversion period and so on.

Suppose â‚¹1000 is borrowed for 2 years at 10% compound interest.

Then, interest for the first year will be

Now, this interest will be added to the original principal giving us â‚¹(1000 + 100) = â‚¹1100.

This will become the principal for the second year. Hence, interest for the second year will be Thus, the total interest for the two years becomes â‚¹210.

If we had used simple interest for the whole period, interest would have been â‚¹200.

Consider the following terms and notations:

** **

Then,

**Note:** In general, if the interest is compounded ** m** times a year, then the amount after

**years will be**

*n*** **

- When interesst is compounded annually but time is in fraction, say years, then
- Âƒ When rates are different for different years, say
*R*_{1}%,*R*_{2}%,*R*_{3}% for 1st, 2nd and 3rd year respectively, then

*P*= â‚¹6000

*R*= 3% p.a.

*n*= 3 years

Amount = â‚¹6,556.362

C.I. = â‚¹(6556.362 - 6000) (Since C.I. =

*A*-

*P*)

C.I. = â‚¹556.362

*P*= â‚¹1000

*A*= â‚¹1331

*R*= 10% p.a.

Time is unknown. Taking time as â€˜

*n*â€™ and substituting values in the formula for amount,

Therefore, the time period comes out to be 3 years.

*P*= â‚¹500

*A*= â‚¹583.20

*n*= 2 years Rate is unknown.

*P*= â‚¹2,000

*R*= 5% p.a.

*n*= 2 years

Interest is being compounded half-yearly which means there are two conversion periods per year. Rate will become

*R*/2 and time will become 2

*n*.

C.I. =

*A*-

*P*= 2207.62 - 2000 = â‚¹207.62

*P*= â‚¹2000,

*R*= 20% p.a.

*n*= 2 years

Interest is compounded quarterly, which means 4 times a year. Hence, rate will become

*R*/4 and conversion periods will be 4

*n*.

*R*= 15%

** **

*P*= â‚¹3,000

*T*= 3 years

*R*

_{1}= 4%

*R*

_{2}= 5%

*R*

_{3}= 6%