##### Reference no: EM131134179

**SIMPLE INTEREST AND COMPUND INTEREST**

**FORMULA OF SIMPLE INTEREST**

SI=P*R*T/100

P=100*SI/R*T

R=100*SI/P*T

T=100*SI/P*R

A=P+SI=P+ (P*T*R)/100=P(1+(R*T)/100)

WHERE P=Principal=Rate of interest per annum,T=Number of years, I=Simple interest and A=Amount.

**Point to Remember:**

Here, the interest is calculated on the original principal. The interest earned on the principal is not taken into account for purpose of calculating interest for later years.

**COMPOUND INTEREST**

In compound interest we consider;

P=Principal

R=Rate percent per unit time

Time=n year

A=Amount

CI=Compound Interest

Then if compound interest is calculated after n year then

A=P (1+R/100) to the power n

CI= P (1+R/100) to the power n-P

**Point to Remember:**

In compound interest the interest is added to the principal at the end of each period *Here are some shortcut formulas for better solving the questions for compound interest:

1) If the rate of interest differs from every year i.e. R1 in first year, R2 in second then

A=P (1+R1/100)(1+R2/100) and so on

2) When the principal changes every year, then we have to calculate compound interest

A=P (1+R/100) to the power n

3) When the principal changes every six months then

A=P (1+(R/2)/100) to the power 2n.

4) When the principal changes every three months then

A=P (1+(R/4)/100) to the power 4n.

5) When the principal changes every month then

A=P (1+(R/12)/100) to the power 12n.

Now we can take some questions and solutions for some unique cases:

**Answer the following question given below:**

Question1:At what rate per cent per annum will a sum of money double in 6 years?

Question2:Find the compound interest on Rs 15000 at 10% per annum for 2.5 years?