# Compound Intrest

**Fast trick to find Compound Intrest**

#####
Q1) Find the effective rate of interest , corresponding to a nominal rate of **10%** per annum.payable half yearly compounding.

### By formula-

**Effective Annual Rate = Yearly rate + (Half-Yearly Rate) ^{2} / 100**

Let the sum be Rs 100

P = Rs 100

r = 10 % Yearly = 5 % Half-Yearly

t = 1 Year = 2 Half - years

Putting the value in formula:

**Effective Annual Rate = Yearly rate + (Half-Yearly Rate) ^{n} / 100**

= 10 + 5^{2} / 100

= 10 + 25 / 100

= 10 + 0.25

= 10 + 0.25

**Effective Annual Rate = 10.25%**

#####
Q2) Manohar deposited Rs **3000** at **6%** p.a. compound interest , Find the compound interest after **2** year?

P = Rs 3000

r = 6 % Yearly

t = n = 2 Year

C.I.= ?

This formula is used only when time is 2 years :

**Compound Interest = ^{P} / _{100} [ 2 * r + r^{2} / 100]**

Putting the value in formula:

= ^{3000} / _{100} [ 2 * 6 + 6^{2} / 100]

= 30 [ 12 + 36 / 100 ]

= 30 [ 12 + 0.36 ]

= 30 * 12.36

= Rs 370.8

**After 2 years Compound interest will be Rs 370.8 **

#####
Q3) The compound interest on a sum at **3000** p.a. for **4%** years is Rs **2**.Find the sum ?

P = P

r = 4 % Yearly

t = n = 2 Year

C.I.= Rs 3000

This formula is used only when time is 2 years :

**Compound Interest = ^{P} / _{100} [ 2 * r + r^{2} / 100]**

Putting the value in formula:

3000 = ^{P} / _{100} [ 2 * 4 + 4^{2} / 100]

3000 = ^{P} / _{100} [ 8 + 16 / 100]

3000 = ^{P} / _{100} [ 8 + 0.16 ]

3000 = ^{P} / _{100} * 8.16

3000 * 100 / 8.16 = P

Rs 36764.705882353 = P

**Sum is Rs 36764.705882353 **

#####
Q4) The sum becomes Rs **1000** in 2 years at **14%** p.a. compound interest .Find the sum ?

P = P

r = 14 % Yearly

t = n = 2 Year

A= Rs 1000

This formula is used only when time is 2 years :

**Compound Interest = ^{P} / _{100} [ 100 + 2 * r + r^{2} / 100]**

Putting the value in formula:

1000 = ^{P} / _{100} [ 100 + 2 * 14 + 14^{2} / 100]

1000 = ^{P} / _{100} [ 128 + 196 / 100]

1000 = ^{P} / _{100} [ 128 + 1.96 ]

1000 = ^{P} / _{100} * 129.96

1000 * 100 / 129.96 = P

Rs 769.4675284703 = P

**Sum is Rs 769.4675284703 **