Interest is defined as the cost of borrowing money as in the case of interest charged on a loan balance. Interest can also be the rate paid for money on deposit as in the case of a certificate of deposit. Interest can be calculated in two ways, simple interest or compound interest.

1. Simple interest

2. Compound interest

**Simple interest** is calculated on the principal, or original, amount of a loan.

**Compound interest** is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as “interest on interest.”

Here we learn Simple interest. Let us first state some terms that we will use in the simple interest.

**Principal (P):** The original sum of money loaned/deposited for a certain period. Also known as capital.

**Interest (I):** The amount of money that you pay to borrow money or the amount of money that you earn on a deposit.

**Time (T):** The duration for which the money is borrowed/deposited.

Rate of Interest (R): The percent of interest that you pay for money borrowed, or earn for money deposited

**What Is Simple Interest?**

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Simple Interest = *Principal x Interest x Time*100

S.I = *P x I x T*100

Where:

P: Principal (original amount)

R: Rate of Interest (in %)

T: Time period (yearly, half-yearly etc.)

From above formula

Principal amount as P = *100 x S.I*R × T

Time as T = *100 x S.I*P × R

Rate as R = *100 x S.I*P × T

The interest is usually paid yearly, half yearly or quarterly as agreed upon.

Amount as A = P + S.I

**Convert to month in year:**

12 months = 1 year

1 months = 1/12 years

9 months = (1 × 9)/12 years

**Practise Problems Related To This Topic**

**(i)Find simple interest on rupees 2000 at 5% per annum for 3 years. Also, find the amount.**

**Solution:**

Principal = 2000 , Rate = 5% per annum. , T = 3 years

By the formula

S.I = *P x I x T*100

= *(2000 × 5 × 3)*100

S.I = 300

** Amount = P + S.I**

Amount = (2000 + 300 )

Amount = 2300

**(ii)Calculate the simple interest on rupees 6400 at 10% p.a. for 9 months.**

**Solution:**

P = 6400 , R = 10% p.a., T = 9 months or 9/12 years

[12 months = 1 year

1 months = 1/12 years

9 months = (1 × 9)/12 years]

By the formula

S.I =

*P x I x T*100

S.I =

*(6400 × 10 × 9)*(100 × 12)

S.I = 480

**(iii) At what percent will rupees 1500 amount to rupees 2400 in 4 years?**

**Solution:**

P = 1500 , R = ? , T= 4 years and, A = 2400

**Amount = P + S.I**

S.I. = A – P

= (2400 – 1500 )

= 900

By the formula

**S.I =**

*P x I x T*100900 =

*(1500 × R × 4)*100

Therefore,

R =

*(900 × 100)*(4 × 1500)

R = 15%

**(iv) James borrowed 24000 from his friend at the rate of 12% per annum for 3 years. At the end of the period, he cleared the account by paying 10640 cash and giving the cow. Find the price of the cow.**

**Solution:**

Here, P = 24000 , R = 12% p.a. , T = 3 years

S.I =

*P x I x T*100

S.I =

*(24000 × 12 × 3)*100

S.I = 8640

**Amount = P + S.I**

Amount = 24000 + 8640 = 32640

10640 + Price of cow = 32460

Therefore,

price of the cow = 32460 – 10640 = 22000

**(v)A sum of money amounts to rupees 9800 after 5 years and rupees 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:**

**Solution:**

Here,

S.I = A – P

S.I. for 3 years = Rs. (12005 – 9800) = Rs. 2205.

S.I. for 5 years = Rs. {(2205/3)* 5} = Rs. 3675.

So, Principal = Rs. (9800 – 3675) = Rs. 6125.

Hence, rate = {(100*3675)/(6125*5)}% = 12%

**(vi)The simple interest on certain sum of money at a certain rate after 5 years for 300. In the next 5 years the principle is tripled, find the total interest obtained at the end of the 10th year?**

**Solution:**

Use the simple interest formula

**S.I =**

*P x I x T*100Where, simple interest directly proportional to principal

(vii) A certain sum of money grows 4 times itself in 5 years. In how many years would it grows to 10 times of itself at the same time?

Solution: By the help of formula:

*N1 – 1*T1 =

*N2 – 1*T2

*4 – 1*5 =

*10 – 1*T2

therefore, T2 =

*9 x 5*3 = 15 years

or

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