##
**Compound
Interest**

**Interest**is the additional sum of money to be paid for the use of money from a bank or money lender for certain period of time. Similarly, if we keep money in a bank or lend to someone else, we will be paid interest.

Interest is calculated on the basis of the initial sum
of money, period of time and the rate of interest. When the interest calculated
for certain sum of money is same for every year, it is called

**simple interest**.
But, when the interest of first year is added to the
principal to calculate the interest of second year, then it is called

**compound interest**.###
**Compound
Interest Formula**

Compound amount and interest are given by the formula,

where, CA ---------------> Compound Amount

CI --------------->
Compound Interest

P --------------->
Principal (initial sum of money)

T --------------->
Time (in year)

R --------------->
Rate of interest (in % per year)

Some other formula,

*1.*

*When the interest is compounded annually with different rates*

**R**for 1_{1}^{st}year,**R**for 2_{2}^{nd}year and**R**for 3_{3}^{rd}year then,*2.*

*When the time is given by ‘*

**T**’ years and ‘**m**’ months then,*3.*

*When interest is compounded half-yearly, then*

###
*Workout
Examples*

*Workout Examples*

*Example 1: Calculate the compound interest and amount when the principal (P) = Rs. 10000, time (T) = 2 years at the rate of interest (R) = 12%.*

*Solution:*

*Here,*

*P = Rs. 10000*

*T = 2 years*

*R = 12%*

*We have,*

*=*

*10000 [(1.12)*^{2}– 1]

*= 10000 × 0.2544*

*= 2544*

*∴*

*CA = P + CI*

*= Rs. 10000 + 2544*

*= Rs. 12544*

*Example 2: At what rate percent per annum compound interest will Rs. 10000 amounts to Rs. 12544 in 2 years?*

*Solution:*

*Here,*

*P = Rs. 10000*

*CA = Rs. 12544*

*T = 2 years*

*We have,*

*or, R = 12%*

*Example 3: In how many years will Rs. 8000 amount to Rs. 13824 at 20% per annum interest compounded yearly?*

*Solution:*

*Here,*

*P = Rs. 8000*

*CA = Rs. 13824*

*T = ?*

*We have,*

*or, 1.728 = (1.2)*^{T}

*or, (1.2)*^{3}= (1.2)^{T}

*∴*

*T = 3 years*

*∴*

*The required time is 3 years.*

*Example 4: Find the difference between compound interest compounded semi-annually and the interest compounded annually on Rs. 8000 at 10% per annum in 1.5 years.*

*Solution:*

*Here,*

*P = Rs. 8000*

*R = 10%*

*T = 1.5 years (1 year 6 months)*

*Now,*

*= 8000 (1.05*^{3}– 1)

*= 8000 × 0.157625*

*= Rs. 1261*

*= 8000 (1.1×1.05 – 1)*

*= 8000 × 0.155*

*= Rs. 1240*

*∴*

*Difference between CI*_{1}and CI_{2}= Rs. 1261 – 1240 = Rs. 21

*Example 5: The compound amount of a sum of money in 3 years is Rs. 13310 and in 4 years is Rs 14641. Find the compound rate of interest per annum and the sum.*

*Solution:*

*Here,*

*CA in 3 years = Rs. 13310*

*or, R = 10%*

*Again, putting R = 10 in equation (i), we get,*

*or, P (1.1)*^{3}= 13310

*or, P = 13310/1.331*

*or, P = Rs. 10000*

*∴*

*The required sum is Rs. 10000 and rate of interest is 10% per annum.*

*You can comment your questions or problems regarding the compound interest here.*

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